{"paper":{"title":"The $\\infty$-eigenvalue problem with a sign-changing weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Joana Terra, Julio D. Rossi, Uriel Kaufmann","submitted_at":"2018-10-12T19:36:25Z","abstract_excerpt":"Let $\\Omega\\subset\\mathbb{R}^{n}$ be a smooth bounded domain and $m\\in C(\\overline{\\Omega})$ be a sign-changing weight function. For $1<p<\\infty$, consider the eigenvalue problem $$\n  \\left\\{ \\begin{array} [c]{ll} -\\Delta_{p}u=\\lambda m(x)|u|^{p-2}u & \\text{in }\\Omega,\\\\ u=0 & \\text{on }\\partial\\Omega, \\end{array} \\right. $$ where $\\Delta_{p}u$ is the usual $p$-Laplacian. Our purpose in this article is to study the limit as $p\\rightarrow\\infty$ for the eigenvalues $\\lambda _{k,p}\\left( m\\right) $ of the aforementioned problem. In addition, we describe the limit of some normalized associated ei"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05696","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"}