{"paper":{"title":"Existence and Regularity of Optimal Shapes for Elliptic Operators with Drift","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AP","authors_text":"Baptiste Trey (CVGI, Bozhidar Velichkov (CVGI), Emmanuel Russ (IF), If)","submitted_at":"2018-10-18T08:29:50Z","abstract_excerpt":"This paper is devoted to the study of shape optimization problems for the first eigenvalue of the elliptic operator with drift L = --$\\Delta$+V (x)\\cdot \\nabla with Dirichlet boundary conditions, where V is a bounded vector field. In the first instance, we prove the existence of a principal eigenvalue $\\lambda$\\_1($\\Omega$, V) for a bounded quasi-open set $\\Omega$ which enjoys similar properties to the case of open sets. Then, given m > 0 and $\\tau$ $\\ge$ 0, we show that the minimum of the following non-variational problem min $\\lambda$\\_1($\\Omega$, V) : $\\Omega$ $\\subset$ D quasi-open, |$\\Ome"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07943","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"}