{"paper":{"title":"Concentration at submanifolds for an elliptic Dirichlet problem near high critical exponents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fethi Mahmoudi, Monica Musso, Shengbing Deng","submitted_at":"2016-06-12T04:16:57Z","abstract_excerpt":"Let $\\Omega$ be a open bounded domain in $\\mathbb{R}^n $ with smooth boundary $\\partial\\Omega$. We consider the equation $ \\Delta u + u^{\\frac{n-k+2}{n-k-2}-\\varepsilon} =0\\,\\hbox{ in }\\,\\Omega $, under zero Dirichlet boundary condition, where $\\varepsilon$ is a small positive parameter. We assume that there is a $k$-dimensional closed, embedded minimal submanifold $K$ of $\\partial\\Omega$, which is non-degenerate, and along which a certain weighted average of sectional curvatures of $\\partial\\Omega$ is negative. Under these assumptions, we prove existence of a sequence $\\varepsilon=\\varepsilon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03666","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"}