{"paper":{"title":"Compactness and existence results for the $p$-Laplace equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Marino Badiale, Michela Guida, Sergio Rolando","submitted_at":"2016-09-18T21:41:52Z","abstract_excerpt":"Given $1<p<N$ and two measurable functions $V\\left( r\\right) \\geq 0$ and $K\\left( r\\right) >0$, $r>0$, 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. We consider exponents $q_{1},q_{2},q$ that can be greater or smaller than $p$. Our r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05556","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"}