{"paper":{"title":"Strong comparison principle for the fractional $p$-Laplacian and applications to starshaped rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Sven Jarohs","submitted_at":"2017-06-05T08:21:10Z","abstract_excerpt":"In the following we show the strong comparison principle for the fractional $p$-Laplacian, i.e. we analyze functions $v,w$ which satisfy $v\\geq w$ in $\\mathbb{R}^N$ and\n  \\[\n  (-\\Delta)^s_pv+q(x)|v|^{p-2}v\\geq (-\\Delta)^s_pw+q(x)|w|^{p-2}w \\quad \\text{in $D$,}\n  \\] where $s\\in(0,1)$, $p>1$, $D\\subset \\mathbb{R}^N$ is an open set, and $q\\in L^{\\infty}(\\mathbb{R}^N)$ is a nonnegative function. Under suitable conditions on $s,p$ and some regularity assumptions on $v,w$ we show that either $v\\equiv w$ in $\\mathbb{R}^N$ or $v>w$ in $D$. Moreover, we apply this result to analyze the geometry of nonn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.01234","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"}