{"paper":{"title":"Wolff's inequality for intrinsic nonlinear potentials and quasilinear elliptic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Igor E. Verbitsky","submitted_at":"2018-12-09T02:42:14Z","abstract_excerpt":"We prove an analogue of Wolff's inequality for the so-called intrinsic nonlinear potentials associated with the quasilinear elliptic equation \\[ -\\Delta_{p} u = \\sigma u^{q} \\quad \\text{in} \\;\\; \\mathbb{R}^n, \\] in the sub-natural growth case $0<q< p-1$, where $\\Delta_{p}u = \\text{div}( |\\nabla u|^{p-2} \\nabla u )$ is the $p$-Laplacian, and $\\sigma$ is a nonnegative measurable function (or measure) on $\\mathbb{R}^n$.\n  As an application, we give a necessary and sufficient condition for the existence of a positive solution $u \\in L^{r}(\\mathbb{R}^{n})$ ($0<r<\\infty$) to this problem, which was "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.03418","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"}