{"paper":{"title":"Schroedinger operators involving singular potentials and measure data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Augusto C. Ponce, Nicolas Wilmet","submitted_at":"2017-05-10T12:17:48Z","abstract_excerpt":"We study the existence of solutions of the Dirichlet problem for the Schroedinger operator with measure data $$ \\left\\{ \\begin{alignedat}{2} -\\Delta u + Vu & = \\mu && \\quad \\text{in } \\Omega,\\\\ u & = 0 && \\quad \\text{on } \\partial \\Omega. \\end{alignedat} \\right. $$ We characterize the finite measures $\\mu$ for which this problem has a solution for every nonnegative potential $V$ in the Lebesgue space $L^p(\\Omega)$ with $1 \\le p \\le N/2$. The full answer can be expressed in terms of the $W^{2,p}$ capacity for $p > 1$, and the $W^{1,2}$ (or Newtonian) capacity for $p = 1$. We then prove the exis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03718","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"}