{"paper":{"title":"A priori bounds for a class of semi-linear degenerate elliptic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Genggeng Huang","submitted_at":"2012-11-18T01:15:46Z","abstract_excerpt":"In this paper, we mainly discuss a priori bounds of the following degenerate elliptic equation, {equation}\\label{000} a^{ij}(x)\\partial_{ij}u+b^i(x)\\partial_i u +f(x,u)=0,\\text{in}\\Omega\\subset\\subset R^n, {equation} where $a^{ij}\\partial_i \\phi\\partial_j \\phi=0$ on $\\partial \\Omega$, $\\phi$ is the defining function of $\\partial \\Omega$. Imposing suitable conditions on the coefficients and $f(x,u)$, one can get the $L^\\infty$-estimates of \\eqref{000} via blow up method."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4180","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"}