{"paper":{"title":"Regularizing effect of absorption terms in singular problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francescantonio Oliva","submitted_at":"2018-10-31T19:33:57Z","abstract_excerpt":"We prove existence of solutions to problems whose model is\n  $$\\begin{cases}\n  \\displaystyle -\\Delta_p u + u^q = \\frac{f}{u^\\gamma} & \\text{in}\\ \\Omega, \\newline\n  u\\ge0 &\\text{in}\\ \\Omega,\\newline\n  u=0 &\\text{on}\\ \\partial\\Omega,\n  \\end{cases}$$\n  where $\\Omega$ is an open bounded subset of $\\mathbb{R}^N$ ($N\\ge2$), $\\Delta_p u$ is the $p$-laplacian operator for $1\\le p <N$, $q>0$, $\\gamma\\ge 0$ and $f$ is a nonnegative function in $L^m(\\Omega)$ for some $m\\ge1$. In particular we analyze the regularizing effect produced by the absorption term in order to infer the existence of finite energy "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.00083","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"}