{"paper":{"title":"The Dirichlet problem for singular elliptic equations with general nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniela Giachetti, Francescantonio Oliva, Francesco Petitta, Virginia De Cicco","submitted_at":"2018-01-10T16:34:39Z","abstract_excerpt":"In this paper, under very general assumptions, we prove existence and regularity of distributional solutions to homogeneous Dirichlet problems of the form $$\\begin{cases} \\displaystyle - \\Delta_{1} u = h(u)f & \\text{in}\\, \\Omega,\\newline u\\geq 0& \\text{in}\\ \\Omega, \\newline u=0 & \\text{on}\\ \\partial \\Omega, \\end{cases} $$ where, $\\Delta_{1} $ is the $1$-laplace operator, $\\Omega$ is a bounded open subset of $\\mathbb{R}^N$ with Lipschitz boundary, $h(s)$ is a continuous function which may become singular at $s=0^{+}$, and $f$ is a nonnegative datum in $L^{N,\\infty}(\\Omega)$ with suitable small "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.03444","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"}