{"paper":{"title":"The effects of a discontinues weight for a problem with a critical nonlinearity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Rejeb Hadiji, Sami Baraket, Yabib Yazidi","submitted_at":"2014-05-29T21:40:05Z","abstract_excerpt":"We study the minimizing problem $\\inf\\left\\{\\displaystyle\\int_{\\Omega}p(x)|\\nabla u|^{2}dx,\\,u\\in H^{1}_{0}(\\Omega),\\,\\|u\\|_{L^{\\frac{2N}{N-2}}(\\Omega)}=1\\right\\}$ where $\\Omega$ is a smooth bounded domain of $\\R^{N}$, $N\\geq 3$ and $p$ a positive discontinuous function. We prove the existence of a minimizer under some assumptions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7734","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"}