{"paper":{"title":"New P\\'olya-Szeg\\\"o-type inequalities and an alternative approach to comparison results for PDE's","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Adele Ferone, Anna Mercaldo, Francesco Chiacchio, Friedemann Brock","submitted_at":"2017-04-06T15:53:13Z","abstract_excerpt":"We prove some P\\'olya-Szeg\\\"o type inequalities which involve couples of functions and their rearrangements. Our inequalities reduce to the classical P\\'olya-Szeg\\\"o principle when the two functions coincide. As an application, we give a different proof of a comparison result for solutions to Dirichlet boundary value problems for Laplacian equations proved by A. Alvino, G. Trombetti, J. I. Diaz and P. L. Lions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01898","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"}