Regularity of minimizers of autonomous convex variational integrals

By Menita Carozza, Jan Kristensen, Antonia Passarelli di Napoli. 2013

63 citations recorded by the source corpus.

We establish local higher integrability and differentiability results for minimizers of variational integrals $$ \mathfrak{F}(v,\Omega) = \int_{\Omega} /! F(Dv(x)) \, dx $$ over $W^{1,p}$--Sobolev mappings $u \colon \Omega \subset {\mathbb R}^n \to {\mathbb R}^N$ satisfying a Dirichlet boundary condition. The integrands $F$ are assumed to be autonomous, convex and of $(p,q)$ growth, but are otherwise not subjected to any further structure conditions, and we consider exponents in the range $1<p \leq q < p^{\ast}$, where $p^{\ast}$ denotes the Sobolev conjugate exponent of $p$.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/b1a87af7a9b7999e8d29943434937b3bf71b02eb

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In Applied Mathematics

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Citations in the corpus

Fully anisotropic elliptic problems with minimally integrable data (2019, background): “They are the topic of diverse contributions, including [17,18,35,41,46,57,61].”
Non-autonomous functionals, borderline cases and related function classes (2016, background): “They have been the object of an intensive investigation during the last years, see for instance [8, 9, 11, 12, 13, 34, 43, 44, 54, 55].”
Recent developments in problems with nonstandard growth and nonuniform ellipticity (2021, background): “In this respect some advance is marked in [49] under additional assumptions.”