{"paper":{"title":"Remarks on the uniqueness for quasilinear elliptic equations with quadratic growth conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Colette De Coster, David Arcoya, Kazunaga Tanaka, Louis Jeanjean","submitted_at":"2013-11-05T06:50:33Z","abstract_excerpt":"In this note we present some uniqueness and comparison results for a class of problem of the form \\begin{equation} \\label{EE0} \\begin{array}{c} - L u = H(x,u,\\nabla u)+ h(x), \\quad u \\in H^1_0(\\Omega) \\cap L^{\\infty}(\\Omega), \\end{array} \\end{equation} where $\\Omega \\subset \\R^N$, $N \\geq 2$ is a bounded domain, $L$ is a general elliptic second order linear operator with bounded coefficients and $H$ is allowed to have a critical growth in the gradient. In some cases our assumptions prove to be sharp."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0975","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"}