{"paper":{"title":"Convergence at infinity for solutions of nonhomogeneous degenerate elliptic equations in exterior domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Filipe Jung dos Santos, Leonardo Prange Bonorino, Lucas Pinto Dutra","submitted_at":"2022-08-23T18:40:49Z","abstract_excerpt":"In this work, first we prove that for any compact set $K\\subset\\mathbb{R}^{n}$ and any continuous function $\\phi$ defined on $\\partial K$, there exists a bounded weak solution in $C(\\bar{\\mathbb{R}^{n}\\backslash K}) \\cap C^1(\\mathbb{R}^{n}\\backslash K)$ to the exterior Dirichlet problem $$ \\begin{cases}\n  -{\\rm div}\\big(\\,|\\nabla u|^{p-2}A(\\,|\\nabla u|\\,)\\nabla u\\,\\big)=f & \\text{ in }\\, \\mathbb{R}^n \\backslash K\n  \\;\\;\\;\\;\\;\\; u = \\phi & \\text{ on } \\partial K\n  \\end{cases}\n  $$ provided $p > n$, $A$ satisfies some growth conditions and $f\\in L^{\\infty}(\\mathbb{R}^n)$ meets a suitable pointwi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.11153","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/2208.11153/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"}