{"paper":{"title":"Supercritical problems on manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Angela Pistoia, Giusi Vaira","submitted_at":"2013-09-10T20:29:44Z","abstract_excerpt":"Let $(M,g)$ be a $m$-dimensional compact Riemannian manifold without boundary. Assume $\\kappa\\in C^2(M)$ is such that $-\\Delta_g+\\kappa$ is coercive. We prove the existence of a solution to the supercritical problems $$ -\\Delta_gu+\\kappa u= u^p,\\ u>0\\quad\\hbox{in}\\ (M,g)\\quad\\hbox{and}\\quad-\\Delta_gu+\\kappa u=\\lambda e^u\\quad\\hbox{in}\\ (M,g) $$ which concentrate s along a $(m-1)-$dimensional submanifold of $M$ as $p\\to\\infty$ and $\\lambda\\to0$, respectively, under suitable symmetry assumptions on the manifold $M$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2661","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"}