{"paper":{"title":"Shape optimization problems on metric measure spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bozhidar Velichkov, Giuseppe Buttazzo","submitted_at":"2013-12-13T19:28:02Z","abstract_excerpt":"We consider shape optimization problems of the form $$\\min\\big\\{J(\\Omega)\\ :\\ \\Omega\\subset X,\\ m(\\Omega)\\le c\\big\\},$$ where $X$ is a metric measure space and $J$ is a suitable shape functional. We adapt the notions of $\\gamma$-convergence and weak $\\gamma$-convergence to this new general abstract setting to prove the existence of an optimal domain. Several examples are pointed out and discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3915","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"}