{"paper":{"title":"Resolutivity and invariance for the Perron method for degenerate equations of divergence type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Abubakar Mwasa, Anders Bj\\\"orn, Jana Bj\\\"orn","submitted_at":"2020-08-03T13:59:50Z","abstract_excerpt":"We consider Perron solutions to the Dirichlet problem for the quasilinear elliptic equation $\\mathop{\\rm div}\\mathcal{A}(x,\\nabla u) = 0$ in a bounded open set $\\Omega\\subset\\mathbf{R}^n$. The vector-valued function $\\mathcal{A}$ satisfies the standard ellipticity assumptions with a parameter $1<p<\\infty$ and a $p$-admissible weight $w$. We show that arbitrary perturbations on sets of $(p,w)$-capacity zero of continuous (and certain quasicontinuous) boundary data $f$ are resolutive and that the Perron solutions for $f$ and such perturbations coincide. As a consequence, we prove that the Perron"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.00883","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2008.00883/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}