{"paper":{"title":"Regularity of minimizers of autonomous convex variational integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Antonia Passarelli di Napoli, Jan Kristensen, Menita Carozza","submitted_at":"2013-10-16T16:20:26Z","abstract_excerpt":"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 $p$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4435","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}