{"paper":{"title":"Sharp estimates on the first Dirichlet eigenvalue of nonlinear elliptic operators via maximum principle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francesco Della Pietra, Giuseppina di Blasio, Nunzia Gavitone","submitted_at":"2017-10-09T15:10:00Z","abstract_excerpt":"In this paper we study optimal lower and upper bounds for functionals involving the first Dirichlet eigenvalue $\\lambda_{F}(p,\\Omega)$ of the anisotropic $p$-Laplacian, $1<p<+\\infty$. Our aim is to enhance how, by means of the $\\mathcal P$-function method, it is possible to get several sharp estimates for $\\lambda_{F}(p,\\Omega)$ in terms of several geometric quantities associated to the domain. The $\\mathcal P$-function method is based on a maximum principle for a suitable function involving the eigenfunction and its gradient."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03140","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"}