{"paper":{"title":"Fading absorption in non-linear elliptic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrey Shishkov, Moshe Marcus","submitted_at":"2012-01-25T17:07:27Z","abstract_excerpt":"We study the equation $-\\Delta u+h(x)|u|^{q-1}u=0$, $q>1$, in $R^N_+=R^{N-1}\\ti R_+$ where $h\\in C(\\bar{R^N_+})$, $h\\geq 0$. Let $(x_1,..., x_N)$ be a coordinate system such that $R^N_+=[x_N>0]$ and denote a point $x\\in \\RN$ by $(x',x_N)$. Assume that $h(x', x_N)>0$ when $x'\\neq 0$ but $h(x',x_N)\\to 0$ as $|x'|\\to 0$. For this class of equations we obtain sharp necessary and sufficient conditions in order that singularities on the boundary do not propagate in the interior."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5325","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"}