{"paper":{"title":"Elliptic problems on the ball endowed with Funk-type metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexandru Krist\\'aly, Imre J. Rudas","submitted_at":"2014-08-06T14:45:24Z","abstract_excerpt":"We study Sobolev spaces on the $n-$dimensional unit ball $B^n(1)$ endowed with a parameter-depending Finsler metric $F_a$, $a\\in [0,1],$ which interpolates between the Klein metric $(a=0)$ and Funk metric $(a=1)$, respectively. We show that the standard Sobolev space defined on the Finsler manifold $(B^n(1),F_a)$ is a vector space if and only if $a\\in [0,1).$ Furthermore, by exploiting variational arguments, we provide non-existence and existence results for sublinear elliptic problems on $(B^n(1),F_a)$ involving the Finsler-Laplace operator whenever $a\\in [0,1).$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1300","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"}