{"paper":{"title":"Compactness results for the $p$-Laplace equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Marino Badiale, Michela Guida, Sergio Rolando","submitted_at":"2015-10-13T20:21:19Z","abstract_excerpt":"Given $1<p<N$ and two measurable functions $V(r)\\geq 0$ and $K(r)>0$, $r>0$, we define the weighted spaces \\[ W=\\left\\{ u\\in D^{1,p}(\\mathbb{R}^N):\\int_{\\mathbb{R}^N}V\\left(\\left|x\\right|\\right) \\left|u\\right|^p dx<\\infty \\right\\} , \\quad L_{K}^q =L^q(\\mathbb{R}^N,K\\left( \\left| x\\right| \\right) dx) \\] and study the compact embeddings of the radial subspace of $W$ into $L_{K}^{q_1}+L_{K}^{q_2}$, and thus into $L_{K}^q$ ($=L_{K}^q+L_{K}^q$) as a particular case. Both exponents $q_1,q_2,q$ greater and lower than $p$ are considered. Our results do not require any compatibility between how the pot"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03879","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"}