{"paper":{"title":"On multiplicity of eigenvalues and symmetry of eigenfunctions of the $p$-Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Benjamin Audoux, Enea Parini, Vladimir Bobkov","submitted_at":"2017-04-11T08:33:58Z","abstract_excerpt":"We investigate multiplicity and symmetry properties of higher eigenvalues and eigenfunctions of the $p$-Laplacian under homogeneous Dirichlet boundary conditions on certain symmetric domains $\\Omega \\subset \\mathbb{R}^N$. By means of topological arguments, we show how symmetries of $\\Omega$ help to construct subsets of $W_0^{1,p}(\\Omega)$ with suitably high Krasnosel'ski\\u{\\i} genus. In particular, if $\\Omega$ is a ball $B \\subset \\mathbb{R}^N$, we obtain the following chain of inequalities: $$ \\lambda_2(p;B) \\leq \\dots \\leq \\lambda_{N+1}(p;B) \\leq \\lambda_\\ominus(p;B). $$ Here $\\lambda_i(p;B)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03194","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"}