{"paper":{"title":"Criticality theory of half-linear equations with the (p,A)-Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Netanel Regev, Yehuda Pinchover","submitted_at":"2014-09-11T08:07:07Z","abstract_excerpt":"We study positive solutions of half-linear second-order elliptic equations of the form $$Q_{A,V}(u):= -\\mathrm{div} (|\\nabla u|_{A}^{p-2}A(x)\\nabla u)+ V(x)|u|^{p-2}u=0 \\quad \\mbox{in }\\Omega,$$ where $1<p<\\infty$, $\\Omega$ is a domain in $\\mathbb{R}^{n}$, $n\\geq 2$, $V\\in L_{\\mathrm{loc}}^{\\infty}(\\Omega)$, $A=\\big(a_{ij}\\big)\\in L_{\\mathrm{loc}}^{\\infty}(\\Omega,\\mathbb{R}^{n^2})$ is a symmetric and locally uniformly positive definite matrix in $\\Omega$, and $$|\\xi|_{A}^{2}:=\\left\\langle A(x)\\xi,\\xi\\right\\rangle=\\sum_{i,j=1}^n a_{ij}(x)\\xi_i\\xi_j \\qquad x\\in \\Omega, \\xi=(\\xi_1,\\ldots,\\xi_n)\\i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3346","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"}