{"paper":{"title":"H\\\"older continuity of bounded, weak solutions of a variational system in the critical case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nirav Shah","submitted_at":"2016-09-14T13:20:07Z","abstract_excerpt":"Let $\\Omega\\subset\\mathbb{R}^{2}$ be a bounded, Lipschitz domain. We consider bounded, weak solutions ($u\\in W^{1, 2}\\cap L^{\\infty}(\\Omega;\\mathbb{R}^N)$) of the vector-valued, Euler-Lagrange system: \\text{div } \\big( A(x, u)Du\\big)=g(x, u, Du)\\quad\\text{in }\\Omega.\n  Under natural growth conditions on the principal part and the inhomogeneity, but without any further restriction on the growth of the inhomogeneity (for example, via a smallness condition), we use a blow-up argument to prove that every bounded, weak solution of the system is H\\\"older continuous. Since the dimension of $\\Omega$ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04256","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"}