# 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]).

## Contents

## 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.

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://www.encyclopediaofmath.org/index.php?title=Camillo.delellis&oldid=32420