{"paper":{"title":"Asymptotics of Dirichlet Problems to Fractional p-Laplacian Functionals-Approach in De Giorgi Sense","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Raphael Feng Li","submitted_at":"2019-07-18T13:03:55Z","abstract_excerpt":"In this paper we firstly study the limit of minimizers of the fractional $W^{s,p}$-norms as $p\\rightarrow+\\infty$ in De Giorgi sense. In particular, we analyzed the $\\Gamma$-convergence of non-homogeneous Dirichlet boundary problem for fractional $p$-Laplacian in this approximation process, and proved that as $p\\rightarrow+\\infty$ the minimizers of fractional $p$-Laplacian with Dirichlet boundary $\\Gamma$-converges to a minimizer of H\\\"{o}lder $\\infty$-Laplacian under the same Dirichlet boundary condition. On the other hand, we first investigate the asymptotic behaviour of non-homogeneous frac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.08028","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"}