{"paper":{"title":"A generalized porous medium equation related to some singular quasilinear problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francesco Petitta","submitted_at":"2014-09-30T11:03:12Z","abstract_excerpt":"In this paper we study existence and nonexistence of solutions for a Dirichlet boundary value problem whose model is $$ \\begin{cases} -\\sum_{m=1}^{\\infty} a_m \\Delta u^m= f&\\text{in}\\ \\Omega \\newline u=0 & \\text{on}\\ \\partial\\Omega\\,, \\end{cases} $$ where $\\Omega$ is a bounded domain of $\\mathbb{R}^N$, $a_m$ is a sequence of nonnegative real numbers, and $f$ is in $L^q(\\Omega)$, $q>\\frac{N}{2}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8479","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"}