View source for User:Camillo.delellis

My [http://user.math.uzh.ch/delellis/ homepage] at the University of Zuerich.

My research interests are in [[Mathematical_analysis | analysis]] and [[Differential_geometry_of_manifolds | differential geometry]],
especially in [[:Category:Partial differential equations | partial differential equations]], 
[[Variational calculus|calculus of variations]], [[Geometric_measure_theory | geometric measure theory]] and [[:Category:Fluid mechanics|fluid mechanics]].
(2010 MSC [http://msc2010.org/mscwiki/index.php?title=35-XX [35xx]], 
[http://msc2010.org/mscwiki/index.php?title=49Jxx [49Jxx]],
[http://msc2010.org/mscwiki/index.php?title=49Qxx [49Qxx]],
[http://msc2010.org/mscwiki/index.php?title=76-XX [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|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]] |

==Some statistics==

[[Special:Statistics|Statistics]] | 
[[Special:PopularPages|Most visited pages]] |
[[Special:RecentChanges|Recent changes]] |
[[:Category:TeX done]] |