{"paper":{"title":"Strong maximum principle for Schr\\\"odinger operators with singular potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Augusto C. Ponce, Luigi Orsina","submitted_at":"2013-11-19T20:00:54Z","abstract_excerpt":"We prove that for every $p > 1$ and for every potential $V \\in L^p$, any nonnegative function satisfying $-\\Delta u + V u \\ge 0$ in an open connected set of $\\mathbb{R}^N$ is either identically zero or its level set $\\{u = 0\\}$ has zero $W^{2, p}$ capacity. This gives an affirmative answer to an open problem of B\\'enilan and Brezis concerning a bridge between Serrin-Stampacchia's strong maximum principle for $p > \\frac{N}{2}$ and Ancona's strong maximum principle for $p = 1$. The proof is based on the construction of suitable test functions depending on the level set $\\{u = 0\\}$ and on the exi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4856","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"}