{"paper":{"title":"Anisotropic singularities to semilienar elliptic equations in a measure framework","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huyuan Chen","submitted_at":"2017-04-17T01:39:18Z","abstract_excerpt":"The purpose of this article is to study very weak solutions of elliptic equation $$ -\\Delta u+g(u)=2k\\frac{\\partial \\delta_0}{\\partial x_N }+j\\delta_0\\quad {\\rm in}\\quad\\ \\ B_1(0),\\qquad u=0\\quad {\\rm on}\\quad\\ \\ \\partial B_1(0), $$ where $k>0$, $j\\ge0$, $B_1(0)$ denotes the unit ball centered at the origin in $\\mathbb{R}^N$ with $N\\geq2$, $g:\\mathbb{R}\\to\\mathbb{R}$ is an odd, nondecreasing and $C^1$ function, $\\delta_0$ is the Dirac mass concentrated at the origin and $\\frac{\\partial\\delta_0}{\\partial x_N}$ is defined in the distribution sense that $$ \\langle\\frac{\\partial \\delta_0}{\\partial"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.04844","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"}