{"paper":{"title":"Sharp estimates and existence for anisotropic elliptic problems with general growth in the gradient","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francesco Della Pietra, Nunzia Gavitone","submitted_at":"2014-02-13T10:51:41Z","abstract_excerpt":"In this paper, we prove sharp estimates and existence results for anisotropic nonlinear elliptic problems with lower order terms depending on the gradient. Our prototype is:\n  $ \\left\\{ \\begin{array}{ll} -\\mathcal Q_{p}u =[H(Du)]^{q}+f(x) &\\text{in }\\Omega,\\\\ u=0&\\text{on }\\partial\\Omega. \\end{array} \\right. $\n  Here $\\Omega$ is a bounded open set of $\\mathbb R^{N}$, $N\\ge 2$, $0<p-1<q\\le p<N$, and $\\mathcal Q_{p}$ is the anisotropic operator $ \\mathcal Q_{p} u ={\\rm div}\\left( [H(Du)]^{p-1}H_{\\xi}(Du) \\right)$, where $H$ is a suitable norm of $\\mathbb R^{N}$. Moreover, $f$ belongs to an appro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3086","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"}