{"paper":{"title":"Regularity and singularities of Optimal Convex shapes in the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Arian Novruzi, Jimmy Lamboley (CEREMADE), Michel Pierre (IRMAR)","submitted_at":"2011-12-13T21:47:53Z","abstract_excerpt":"We focus here on the analysis of the regularity or singularity of solutions $\\Om_{0}$ to shape optimization problems among convex planar sets, namely: $$ J(\\Om_{0})=\\min\\{J(\\Om),\\ \\Om\\ \\textrm{convex},\\ \\Omega\\in\\mathcal S_{ad}\\}, $$ where $\\mathcal S_{ad}$ is a set of 2-dimensional admissible shapes and $J:\\mathcal{S}_{ad}\\rightarrow\\R$ is a shape functional. Our main goal is to obtain qualitative properties of these optimal shapes by using first and second order optimality conditions, including the infinite dimensional Lagrange multiplier due to the convexity constraint. We prove two types o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3054","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"}