{"paper":{"title":"Blow-up solutions for some nonlinear elliptic equations involving a Finsler-Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francesco Della Pietra, Giuseppina di Blasio","submitted_at":"2015-02-24T11:27:13Z","abstract_excerpt":"In this paper we prove existence results and asymptotic behavior for strong solutions $u\\in W^{2,2}_{\\textrm{loc}}(\\Omega)$ of the nonlinear elliptic problem \\begin{equation} \\tag{P} \\label{abstr} \\left\\{ \\begin{array}{ll} -\\Delta_{H}u+H(\\nabla u)^{q}+\\lambda u=f&\\text{in }\\Omega,\\\\ u\\rightarrow +\\infty &\\text{on }\\partial\\Omega, \\end{array} \\right. \\end{equation} where $H$ is a suitable norm of $\\mathbb R^{n}$, $\\Omega$ is a bounded domain, $\\Delta_{H}$ is the Finsler Laplacian, $1<q\\le 2$, $\\lambda>0$ and $f$ is a suitable function in $L^{\\infty}_{\\textrm{loc}}$. Furthermore, we are interest"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06768","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"}