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[http://msc2010.org/mscwiki/index.php?title=76-XX [76xx]]).
 
[http://msc2010.org/mscwiki/index.php?title=76-XX [76xx]]).
  
−
==Pages of which I am contributor and I am "watching"==
+
==Pages to which I have contributed and on my "watch-list"==
  
 +
[[Abel criterion]] |
 +
[[Abel transformation]] |
 
[[Absolute continuity]] |
 
[[Absolute continuity]] |
 
[[Absolutely continuous measures]] |
 
[[Absolutely continuous measures]] |
Line 18: Line 20:
 
[[Additive class of sets]] |
 
[[Additive class of sets]] |
 
[[Algebra of sets]] |
 
[[Algebra of sets]] |
 +
[[Analytic function]] |
 +
[[Anger function]] |
 
[[Approximate continuity]] |
 
[[Approximate continuity]] |
 
[[Approximate derivative]] |
 
[[Approximate derivative]] |
Line 27: Line 31:
 
[[Baire space]] |
 
[[Baire space]] |
 
[[Baire theorem]] |
 
[[Baire theorem]] |
 +
[[Bernstein problem in differential geometry]] |
 +
[[Bernstein theorem]] |
 +
[[Bertrand criterion]] |
 +
[[Bessel equation]] |
 +
[[Bessel functions]] |
 
[[Borel field of events]] |
 
[[Borel field of events]] |
 
[[Borel field of sets]] |
 
[[Borel field of sets]] |
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[[Borel system of sets]] |
 
[[Borel system of sets]] |
 
[[Carathéodory measure]] |
 
[[Carathéodory measure]] |
 +
[[Casorati-Sokhotskii-Weierstrass theorem]] |
 
[[Category of a set]] |
 
[[Category of a set]] |
 +
[[Catenoid]] |
 +
[[Cauchy criteria]] |
 +
[[Cauchy integral theorem]] |
 +
[[Cauchy kernel]] |
 +
[[Cauchy-Riemann equations]] |
 +
[[Cauchy sequence]] |
 +
[[Cauchy test]] |
 +
[[Cochain]] |
 +
[[Complete metric space]] |
 +
[[Complete uniform space]] |
 +
[[Completion]] |
 +
[[Continuity, modulus of]] |
 
[[Convergence of measures]] |  
 
[[Convergence of measures]] |  
 +
[[Cylinder functions]] |
 +
[[D'Alembert criterion (convergence of series)]] |
 +
[[Dedekind criterion (convergence of series)]] |
 
[[De la Vallee-Poussin criterion]] |
 
[[De la Vallee-Poussin criterion]] |
 
[[Dense set]] |
 
[[Dense set]] |
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[[Dini criterion]] |
 
[[Dini criterion]] |
 
[[Dini-Lipschitz criterion]] |
 
[[Dini-Lipschitz criterion]] |
 +
[[Dirichlet criterion (convergence of series)]] |
 +
[[Discontinuity point]] |
 +
[[Divergence theorem]] |
 +
[[Du Bois-Reymond criterion (convergence of series)]] |
 
[[Egorov theorem]] |
 
[[Egorov theorem]] |
 +
[[Ermakov convergence criterion]] |
 +
[[Essential singular point]] |
 
[[Favard measure]] |
 
[[Favard measure]] |
 
[[Field of sets]] |
 
[[Field of sets]] |
 +
[[First integral]] |
 +
[[Flux of a vector field]] |
 +
[[Gauss criterion]] |
 
[[Generic set]] |
 
[[Generic set]] |
 
[[Hahn decomposition]] |
 
[[Hahn decomposition]] |
 +
[[Hankel functions]] |
 +
[[Hardy spaces]] |
 
[[Hardy variation]] |
 
[[Hardy variation]] |
 +
[[Hartogs theorem]] |
 
[[Hausdorff dimension]] |
 
[[Hausdorff dimension]] |
 
[[Hausdorff measure]] |
 
[[Hausdorff measure]] |
 +
[[Helicoid]] |
 
[[Improper integral]] |
 
[[Improper integral]] |
 
[[Integration by substitution]] |
 
[[Integration by substitution]] |
Line 59: Line 97:
 
[[Jordan decomposition (of a measure)]] |
 
[[Jordan decomposition (of a measure)]] |
 
[[Jump function]] |
 
[[Jump function]] |
 +
[[Korn inequality]] |
 +
[[Kummer criterion]] |
 +
[[Lagrange function]] |
 +
[[Lagrange multipliers]] |
 
[[Lebesgue criterion]] |
 
[[Lebesgue criterion]] |
 
[[Lebesgue decomposition]] |
 
[[Lebesgue decomposition]] |
 
[[Lebesgue point]] |
 
[[Lebesgue point]] |
 +
[[Lipschitz condition]] |
 +
[[Lipschitz constant]] |
 +
[[Lipschitz function]] |
 +
[[Lobachevskii criterion (for convergence)]] |
 +
[[Logarithmic convergence criterion]] |
 +
[[Mathematical symbols]] |
 
[[Minor]] |
 
[[Minor]] |
 +
[[Morera theorem]] |
 +
[[Morse lemma]] |
 
[[Negative variation of a function]] |
 
[[Negative variation of a function]] |
 +
[[Neumann function]] |
 +
[[Newton-Leibniz formula]] |
 
[[Nowhere-dense set]] |
 
[[Nowhere-dense set]] |
 +
[[Peano theorem]] |
 +
[[Perimeter]] |
 +
[[Perfect set]] |
 
[[Pierpont variation]] |
 
[[Pierpont variation]] |
 
[[Positive variation of a function]] |
 
[[Positive variation of a function]] |
 +
[[Raabe criterion]] |
 
[[Radon measure]] |  
 
[[Radon measure]] |  
 
[[Radon-Nikodým theorem]] |
 
[[Radon-Nikodým theorem]] |
 
[[Rectifiable curve]] |
 
[[Rectifiable curve]] |
 
[[Regular set function]] |
 
[[Regular set function]] |
 +
[[Removable singular point]] |
 
[[Ring of sets]] |
 
[[Ring of sets]] |
 
[[Sard theorem]] |
 
[[Sard theorem]] |
 
[[Semicontinuous function]] |
 
[[Semicontinuous function]] |
 +
[[Scherk surface]] |
 
[[Set function]] |
 
[[Set function]] |
 
[[Signed measure]] |
 
[[Signed measure]] |
 +
[[Simply-connected domain]] |
 
[[Singular function]] |
 
[[Singular function]] |
 
[[Singular measures]] |
 
[[Singular measures]] |
 +
[[Stokes theorem]] |
 +
[[Struve function]] |
 
[[Support of a function]] |
 
[[Support of a function]] |
 
[[Support of a measure]] |
 
[[Support of a measure]] |
 +
[[Taylor series]] |
 
[[Tight measure]] |
 
[[Tight measure]] |
 
[[Tonelli plane variation]] |
 
[[Tonelli plane variation]] |
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[[Variation of a function]] |
 
[[Variation of a function]] |
 
[[Vitali variation]] |
 
[[Vitali variation]] |
 +
[[Volume form]] |
 +
[[Weak convergence of probability measures]] |
 +
[[Weber function]] |
 
[[Young criterion]] |
 
[[Young criterion]] |
  
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[[Atom]] |
 
[[Atom]] |
 
[[Cantor ternary function]] |
 
[[Cantor ternary function]] |
 +
[[Cauchy-Lipschitz theorem]] |
 
[[Change of variables in an integral]] |
 
[[Change of variables in an integral]] |
 
[[Coarea formula]] |
 
[[Coarea formula]] |
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[[Differentiation of measures]] |  
 
[[Differentiation of measures]] |  
 
[[Function of bounded variation]] |
 
[[Function of bounded variation]] |
 +
[[Gronwall lemma]] |
 
[[Heaviside function]] |
 
[[Heaviside function]] |
 +
[[Integral test]] |
 +
[[Inverse function]] |
 
[[Kirszbraun theorem]] |
 
[[Kirszbraun theorem]] |
 +
[[Leibniz rule]] |
 +
[[Lojasiewicz inequality]] |
 +
[[Osgood criterion]] |
 
[[Outer measure]] |
 
[[Outer measure]] |
 +
[[Proper map]] |
 
[[Rademacher theorem]] |
 
[[Rademacher theorem]] |
 +
[[Real analytic function]] |
 
[[Rectifiable set]] |  
 
[[Rectifiable set]] |  
−
[[Riesz representation theorem]]
+
[[Regular value]] |
 +
[[Riesz representation theorem]] |
 +
[[Simons cone]] |
 +
[[Simons inequality]] |
 +
[[Stepanov theorem]] |
  
 
==Pages which need to be created==
 
==Pages which need to be created==
  
 
[[Baire measure]] |
 
[[Baire measure]] |
−
[[Cauchy product]] |  
+
[[Cauchy product]] |
 +
[[Completely integrable system]]
 
[[Covering theorems (measure theory)]] |
 
[[Covering theorems (measure theory)]] |
 +
[[Disintegration of measures]] |
 
[[Frostman's Lemma]] |
 
[[Frostman's Lemma]] |
 
[[Gamma-convergence]] |
 
[[Gamma-convergence]] |
 +
[[Gradient flow]] |
 +
[[Hodge star]] |
 
[[Koch curve]] |
 
[[Koch curve]] |
 
[[Lp spaces]] |
 
[[Lp spaces]] |
 +
[[Lyapunov-Schmidt reduction]] |
 
[[Mass transport]] |
 
[[Mass transport]] |
 
[[Metric geometry]] |
 
[[Metric geometry]] |
 
[[Mumford-Shah functional]] |
 
[[Mumford-Shah functional]] |
−
[[Partial differential equation]] |
+
[[Nash-Moser iteration]] |
 +
[[Partition of unity]] |
 
[[Polish space]] |
 
[[Polish space]] |
 
[[Principal value]] |
 
[[Principal value]] |
 +
[[Removable singularity]] |
 
[[Sobolev inequality]] |
 
[[Sobolev inequality]] |
 +
[[Transport equationt]] |
 
[[Weak-star topology|Weak$^\star$ topology]]
 
[[Weak-star topology|Weak$^\star$ topology]]
  
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[[Banach-Steinhaus theorem]] |
 
[[Banach-Steinhaus theorem]] |
 
[[Barrier]] |
 
[[Barrier]] |
−
[[Bernstein theorem]] |
 
 
[[Birkhoff-Rott equation]] |
 
[[Birkhoff-Rott equation]] |
 
[[Boundary layer]] |
 
[[Boundary layer]] |
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[[Cantor set]] |
 
[[Cantor set]] |
 
[[Capacity]] |
 
[[Capacity]] |
−
[[Catenoid]] |
 
 
[[Cauchy problem]] |
 
[[Cauchy problem]] |
 
[[Class of differentiability]] |
 
[[Class of differentiability]] |
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[[Differential form]] |
 
[[Differential form]] |
 
[[Differential geometry]] |
 
[[Differential geometry]] |
 +
[[Differential inequality]] |
 
[[Differentiation]] |
 
[[Differentiation]] |
 
[[Diffusion equation]] |
 
[[Diffusion equation]] |
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[[Green function]] |
 
[[Green function]] |
 
[[H-principle]] |
 
[[H-principle]] |
−
[[Hardy spaces]] |
 
 
[[Harmonic analysis]] |
 
[[Harmonic analysis]] |
 
[[Harmonic function]] |
 
[[Harmonic function]] |
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[[Harnack inequality]] |
 
[[Harnack inequality]] |
 
[[Heat equation]] |
 
[[Heat equation]] |
−
[[Helicoid]] |
 
 
[[Helmholtz equation]] |
 
[[Helmholtz equation]] |
 
[[Hyperbolic partial differential equation]] |
 
[[Hyperbolic partial differential equation]] |
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[[Kernel of an integral operator]] |
 
[[Kernel of an integral operator]] |
 
[[Kinetic equation]] |
 
[[Kinetic equation]] |
−
[[Korn inequality]] |
 
 
[[Laplace equation]] |
 
[[Laplace equation]] |
 
[[Lebesgue integral]] |
 
[[Lebesgue integral]] |
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[[Linear partial differential equation]] |
 
[[Linear partial differential equation]] |
 
[[Liouville theorems]] |
 
[[Liouville theorems]] |
−
[[Lipschitz condition]] |
 
 
[[Luzin-C-property]] |
 
[[Luzin-C-property]] |
 
[[Luzin criterion]] |
 
[[Luzin criterion]] |
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[[Parabolic partial differential equation]] |
 
[[Parabolic partial differential equation]] |
 
[[Partial differential equations on a manifold]] |
 
[[Partial differential equations on a manifold]] |
−
[[Perfect set]] |
 
 
[[Perron method]] |
 
[[Perron method]] |
 
[[Plateau problem]] |
 
[[Plateau problem]] |
 
[[Plateau problem, multi-dimensional]] |
 
[[Plateau problem, multi-dimensional]] |
−
[[Poincaré inequality]] |[[Poincaré inequality]] |
+
[[Poincaré inequality]] |
 
[[Poisson equation]] |
 
[[Poisson equation]] |
 
[[Riemannian curvature]] |
 
[[Riemannian curvature]] |
 
[[Saddle point]] |
 
[[Saddle point]] |
 
[[Schauder theorem]] |
 
[[Schauder theorem]] |
−
[[Scherk surface]] |
 
 
[[Second fundamental form]] |
 
[[Second fundamental form]] |
 
[[Series]] |
 
[[Series]] |
 
[[Shock waves, mathematical theory of]] |
 
[[Shock waves, mathematical theory of]] |
 
[[Sobolev generalized derivative]] |
 
[[Sobolev generalized derivative]] |
−
[[Stokes formula]] |
 
−
[[Stokes theorem]] |
 
 
[[Strong solution]] |
 
[[Strong solution]] |
 
[[Subdifferential]] |
 
[[Subdifferential]] |
 +
[[Subharmonic function]] |
 
[[Superharmonic function]] |
 
[[Superharmonic function]] |
 
[[Turbulence, mathematical problems in]] |
 
[[Turbulence, mathematical problems in]] |
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[[Viscosity solutions]] |
 
[[Viscosity solutions]] |
 
[[Vitali theorem]] |
 
[[Vitali theorem]] |
−
[[Weak convergence of probability measures]] |
 
 
[[Weak derivative]] |
 
[[Weak derivative]] |
 
[[Weak topology]] |
 
[[Weak topology]] |
 +
[[Weierstrass representation of a minimal surface]] |
 
[[Young measure]] |
 
[[Young measure]] |
  

Latest revision as of 07:40, 12 July 2014

My homepage at the University of Zuerich.

My research interests are in analysis and differential geometry, especially in partial differential equations, calculus of variations, geometric measure theory and fluid mechanics. (2010 MSC [35xx], [49Jxx], [49Qxx], [76xx]).

Pages to which I have contributed and on my "watch-list"

Abel criterion | Abel transformation | Absolute continuity | Absolutely continuous measures | Absolutely convergent improper integral | Absolutely convergent series | Absolutely integrable function | Additive class of sets | Algebra of sets | Analytic function | Anger function | Approximate continuity | Approximate derivative | Approximate differentiability | Approximate limit | Arzelà variation | Baire classes | Baire property | Baire space | Baire theorem | Bernstein problem in differential geometry | Bernstein theorem | Bertrand criterion | Bessel equation | Bessel functions | Borel field of events | Borel field of sets | Borel function | Borel measure | Borel set | Borel system of sets | Carathéodory measure | Casorati-Sokhotskii-Weierstrass theorem | Category of a set | Catenoid | Cauchy criteria | Cauchy integral theorem | Cauchy kernel | Cauchy-Riemann equations | Cauchy sequence | Cauchy test | Cochain | Complete metric space | Complete uniform space | Completion | Continuity, modulus of | Convergence of measures | Cylinder functions | D'Alembert criterion (convergence of series) | Dedekind criterion (convergence of series) | De la Vallee-Poussin criterion | Dense set | Density topology | Dini criterion | Dini-Lipschitz criterion | Dirichlet criterion (convergence of series) | Discontinuity point | Divergence theorem | Du Bois-Reymond criterion (convergence of series) | Egorov theorem | Ermakov convergence criterion | Essential singular point | Favard measure | Field of sets | First integral | Flux of a vector field | Gauss criterion | Generic set | Hahn decomposition | Hankel functions | Hardy spaces | Hardy variation | Hartogs theorem | Hausdorff dimension | Hausdorff measure | Helicoid | Improper integral | Integration by substitution | Integration by parts | Jacobi matrix | Jacobian | Jordan criterion | Jordan decomposition (of a function) | Jordan decomposition (of a signed measure) | Jordan decomposition (of a measure) | Jump function | Korn inequality | Kummer criterion | Lagrange function | Lagrange multipliers | Lebesgue criterion | Lebesgue decomposition | Lebesgue point | Lipschitz condition | Lipschitz constant | Lipschitz function | Lobachevskii criterion (for convergence) | Logarithmic convergence criterion | Mathematical symbols | Minor | Morera theorem | Morse lemma | Negative variation of a function | Neumann function | Newton-Leibniz formula | Nowhere-dense set | Peano theorem | Perimeter | Perfect set | Pierpont variation | Positive variation of a function | Raabe criterion | Radon measure | Radon-Nikodým theorem | Rectifiable curve | Regular set function | Removable singular point | Ring of sets | Sard theorem | Semicontinuous function | Scherk surface | Set function | Signed measure | Simply-connected domain | Singular function | Singular measures | Stokes theorem | Struve function | Support of a function | Support of a measure | Taylor series | Tight measure | Tonelli plane variation | Totally-additive function | Upper and lower limits | Variation of a function | Vitali variation | Volume form | Weak convergence of probability measures | Weber function | Young criterion |

Pages I started ex novo

Area formula | Atom | Cantor ternary function | Cauchy-Lipschitz theorem | Change of variables in an integral | Coarea formula | Density of a set | Differentiation of measures | Function of bounded variation | Gronwall lemma | Heaviside function | Integral test | Inverse function | Kirszbraun theorem | Leibniz rule | Lojasiewicz inequality | Osgood criterion | Outer measure | Proper map | Rademacher theorem | Real analytic function | Rectifiable set | Regular value | Riesz representation theorem | Simons cone | Simons inequality | Stepanov theorem |

Pages which need to be created

Baire measure | Cauchy product | Completely integrable system Covering theorems (measure theory) | Disintegration of measures | Frostman's Lemma | Gamma-convergence | Gradient flow | Hodge star | Koch curve | Lp spaces | Lyapunov-Schmidt reduction | Mass transport | Metric geometry | Mumford-Shah functional | Nash-Moser iteration | Partition of unity | Polish space | Principal value | Removable singularity | Sobolev inequality | Transport equationt | Weak$^\star$ topology

Pages which need to be expanded

Sobolev space

The page contains very little apart from the definition. In particular it lacks: alternative definitions; approximation properties; product and chain rules; trace theorems; extension theorems; Morrey, Sobolev and Poincaré inequalities; embedding theorems; approximate continuity; approximate differentiability; variants (e.g. $W^{1,p}_0$, spaces used for the Stokes operator); fractional (Sobolev-Slobodecky) and negative spaces; capacity; recent extensions to general targets and general domains.


Further pages related to my mathematical interests

And which I will take a look at and most likely modify (sooner or later!).

Absolute summability | Aerodynamics, mathematical problems of | Affine minimal surface | Arzelà-Ascoli theorem | Banach-Mazur game | Banach-Steinhaus theorem | Barrier | Birkhoff-Rott equation | Boundary layer | Boundary value problem, elliptic equations | Boundary value problem, partial differential equations | Cantor set | Capacity | Cauchy problem | Class of differentiability | Conjugate function | Convergence, types of | Convergence of distributions | Convex functional | Convex integration | Convolution of functions | Current | Curl | Darboux-Baire-1-function | Delta-function | Deformation, isometric | Derivative | Diameter | Differential | Differential calculus | Differential equation, partial | Differential equation, partial, of the first order | Differential equation, partial, of the second order | Differential equation, partial, variational methods | Differential form | Differential geometry | Differential inequality | Differentiation | Diffusion equation | Dirac delta-function | Dirichlet Laplacian | Dirichlet principle | Dirichlet problem | Distribution | Divergence | Eikonal equation | Elliptic partial differential equation | Energy inequality | Energy integral | Euler equation | Fatou theorem (on Lebesgue integrals) | Federer-Fleming deformation theorem | First variation | Fixed point | Flat norm | Fractals | Fubini theorem | Functional analysis | Galilean transformation | Gas dynamics, equations of | Gaussian curvature | Generalized derivative | Generalized function | Generalized function, derivative of a | Generalized functions, product of | Generalized functions, space of | Geometric measure theory | Gradient | Gradient method | Green formulas | Green function | H-principle | Harmonic analysis | Harmonic function | Harmonic polynomial | Harnack inequality | Heat equation | Helmholtz equation | Hyperbolic partial differential equation | Hölder condition | Hölder inequality | Hölder space | Integrability | Integral | Isometric immersion | Isoperimetric inequality | Isoperimetric inequality, classical | Isoperimetric problem | Isothermal coordinates | John-Nirenberg inequalities | Kernel of an integral operator | Kinetic equation | Laplace equation | Lebesgue integral | Lebesgue measure | Lebesgue theorem | Length | Line (curve) | Linear differential operator | Linear elliptic partial differential equation and system | Linear partial differential equation | Liouville theorems | Luzin-C-property | Luzin criterion | Luzin-N-property | Luzin theorem | Mass and co-mass | Maximum principle | Measurable function | Measurable set | Measure | Metric space | Minimal surface | Minimax principle | Monge-Ampère equation | Moser-Trudinger inequality | Nash theorems (in differential geometry) | Navier-Stokes equations | Newton method | Nikodym boundedness theorem | Nikodym convergence theorem | Non-linear differential equation | Non-linear partial differential equation | Non-measurable set | One-parameter semi-group | Parabolic partial differential equation | Partial differential equations on a manifold | Perron method | Plateau problem | Plateau problem, multi-dimensional | Poincaré inequality | Poisson equation | Riemannian curvature | Saddle point | Schauder theorem | Second fundamental form | Series | Shock waves, mathematical theory of | Sobolev generalized derivative | Strong solution | Subdifferential | Subharmonic function | Superharmonic function | Turbulence, mathematical problems in | Variational calculus | Variational calculus in the large | Variational problem | Vector measure | Viscosity | Viscosity solutions | Vitali theorem | Weak derivative | Weak topology | Weierstrass representation of a minimal surface | Young measure |

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How to Cite This Entry:
Camillo.delellis. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Camillo.delellis&oldid=30449
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