{"paper":{"title":"On Yamabe type problems on Riemannian manifolds with boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Angela Pistoia, Anna Maria Micheletti, Marco Ghimenti","submitted_at":"2015-06-30T14:25:19Z","abstract_excerpt":"Let $(M,g)$ be a $n-$dimensional compact Riemannian manifold with boundary. We consider the Yamabe type problem \\begin{equation} \\left\\{ \\begin{array}{ll} -\\Delta_{g}u+au=0 & \\text{ on }M \\\\ \\partial_\\nu u+\\frac{n-2}{2}bu= u^{{n\\over n-2}\\pm\\varepsilon} & \\text{ on }\\partial M \\end{array}\\right. \\end{equation} where $a\\in C^1(M),$ $b\\in C^1(\\partial M)$, $\\nu$ is the outward pointing unit normal to $\\partial M $ and $\\varepsilon$ is a small positive parameter. We build solutions which blow-up at a point of the boundary as $\\varepsilon$ goes to zero. The blowing-up behavior is ruled by the func"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.09105","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"}