{"paper":{"title":"Regularity for free interface variational problems in a general class of gradients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.OC","authors_text":"Adolfo Arroyo-Rabasa","submitted_at":"2016-03-03T00:28:36Z","abstract_excerpt":"We present a way to study a wide class of optimal design problems with a perimeter penalization. More precisely, we address existence and regularity properties of saddle points of energies of the form $$ (u,A) \\quad \\mapsto \\quad \\int_\\Omega 2fu \\; \\text{d}x \\; - \\int_{\\Omega \\cap A} \\sigma_1 \\mathscr A u \\cdot \\mathscr A u \\; \\text{d}x \\; - \\int_{\\Omega \\setminus A} \\sigma_2\\mathscr A u\\cdot \\mathscr A u \\; \\text{d}x \\; + \\; \\text{Per}(A;\\overline \\Omega),$$ where $\\Omega$ is a bounded Lipschitz domain, $A\\subset \\mathbb R^N$ is a Borel set, $u:\\Omega \\subset \\mathbb R^N \\to \\mathbb R^d$, $\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00940","kind":"arxiv","version":2},"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"}