{"paper":{"title":"Spectral optimization problems for potentials and measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.OC","authors_text":"Bozhidar Velichkov, Dorin Bucur, Giuseppe Buttazzo","submitted_at":"2013-10-06T10:04:49Z","abstract_excerpt":"In the present paper we consider spectral optimization problems involving the Schr\\\"odinger operator $-\\Delta +\\mu$ on $\\R^d$, the prototype being the minimization of the $k$ the eigenvalue $\\lambda_k(\\mu)$. Here $\\mu$ may be a capacitary measure with prescribed torsional rigidity (like in the Kohler-Jobin problem) or a classical nonnegative potential $V$ which satisfies the integral constraint $\\ds \\int V^{-p}dx \\le m$ with $0<p<1$. We prove the existence of global solutions in $\\R^d$ and that the optimal potentials or measures are equal to $+\\infty$ outside a compact set."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1568","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"}