{"paper":{"title":"Homogenization of a Dirichlet semilinear elliptic problem with a strong singularity at $u=0$ in a domain with many small holes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniela Giachetti, Fran\\c{c}ois Murat, Pedro J. Mart\\'inez-Aparicio","submitted_at":"2017-05-26T10:53:33Z","abstract_excerpt":"We perform the homogenization of the semilinear elliptic problem\n  \\begin{equation*} \\begin{cases} u^\\varepsilon \\geq 0 & \\mbox{in} \\; \\Omega^\\varepsilon,\\\\ \\displaystyle - div \\,A(x) D u^\\varepsilon = F(x,u^\\varepsilon) & \\mbox{in} \\; \\Omega^\\varepsilon,\\\\ u^\\varepsilon = 0 & \\mbox{on} \\; \\partial \\Omega^\\varepsilon.\\\\ \\end{cases} \\end{equation*} In this problem $F(x,s)$ is a Carath\\'eodory function such that $0 \\leq F(x,s) \\leq h(x)/\\Gamma(s)$ a.e. $x\\in\\Omega$ for every $s > 0$, with $h$ in some $L^r(\\Omega)$ and $\\Gamma$ a $C^1([0, +\\infty[)$ function such that $\\Gamma(0) = 0$ and $\\Gamma'"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09527","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"}