User:Camillo.delellis

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 of which I am contributor and I am "watching"

Absolute continuity | Absolutely continuous measures | Absolutely convergent series | Algebra of sets | Approximate continuity | Approximate derivative | Approximate differentiability | Approximate limit | Arzelà variation | Baire space | Baire theorem | Borel measure | Borel function | Borel set | Carathéodory measure | Category of a set | Convergence of measures | Dense set | Hahn decomposition | Hardy variation | Jacobian | Jordan criterion | Jordan decomposition (of a function) | Jordan decomposition (of a signed measure) | Jordan decomposition (of a measure) | Jump function | Lebesgue decomposition | Lebesgue point | Negative variation of a function | Nowhere-dense set Pierpont variation | Positive variation of a function | Radon measure | Radon-Nikodým theorem | Rectifiable curve | Regular set function | Ring of sets | Semicontinuous function | Set function | Signed measure | Singular function | Singular measures | Tonelli plane variation | Upper and lower limits | Variation of a function | Vitali variation |

Pages I started ex novo

Atom | Cantor ternary function | Density of a set | Differentiation of measures | Function of bounded variation | Outer measure | Rademacher theorem | Rectifiable set | Riesz representation theorem

Pages which need to be created

Area formula | Baire measure | Cauchy product | Change of variables formula | Coarea formula | Covering theorems (measure theory) | Gamma-convergence | Heaviside function | Kirszbraun theorem | Mass transport | Mumford-Shah functional | Poincaré inequality | Polish space | Sobolev inequality | 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 | Absolutely integrable function | Aerodynamics, mathematical problems of | Affine minimal surface | Arzelà-Ascoli theorem | Baire classes | Baire property | Banach-Mazur game | Banach-Steinhaus theorem | Barrier | Bernstein theorem | Birkhoff-Rott equation | Boundary layer | Boundary value problem, elliptic equations | Boundary value problem, partial differential equations | Cantor set | Capacity | Catenoid | 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 | 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 | Differentiation | Diffusion equation | Dirac delta-function | Dirichlet Laplacian | Dirichlet principle | Dirichlet problem | Distribution | Divergence | Egorov theorem | 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 | Hardy spaces | Harmonic analysis | Harmonic function | Harmonic polynomial | Harnack inequality | Hausdorff dimension | Hausdorff measure | Heat equation | Helicoid | Helmholtz equation | Hyperbolic partial differential equation | Hölder condition | Hölder inequality | Hölder space | Integrability | Integral | Integration by parts | Isometric immersion | Isoperimetric inequality | Isoperimetric inequality, classical | Isoperimetric problem | Isothermal coordinates | Jacobi matrix | John-Nirenberg inequalities | Kernel of an integral operator | Kinetic equation | Korn inequality | 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 | Lipschitz condition | 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 | Poisson equation | Riemannian curvature | Saddle point | Schauder theorem | Scherk surface | Second fundamental form | Series | Shock waves, mathematical theory of | Sobolev generalized derivative | Stokes formula | Stokes theorem | Strong solution | Subdifferential | Support of a measure | Superharmonic function | Turbulence, mathematical problems in | Variational calculus | Variational calculus in the large | Variational problem | Vector measure | Viscosity | Viscosity solutions | Vitali theorem | Weak convergence of probability measures | Weak derivative | Weak topology | Young measure |

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