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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'"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1705.09527","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-26T10:53:33Z","cross_cats_sorted":[],"title_canon_sha256":"3575d12971fe630ae13afa1d7354af971c5da4be76d8d96552cc0dd131372fdf","abstract_canon_sha256":"0f91ebd773f72f62018a3ffada22c3ad2ee1c538e0ed0e9f4fb9d413c9e86c87"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:38.437781Z","signature_b64":"c60Wde0lcL2Wjbht8PWQO/ZdxgfUBZF3k07pVSlWRD9oJYnIkcUo6q6Oxq7gj95EfnJWWCNBJFiVd559wQ+PBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ba3ab3a279fd92691c781fe251328b3ccac95890c972d587b8766017615fc94","last_reissued_at":"2026-05-18T00:43:38.437334Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:38.437334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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