{"paper":{"title":"Continuity of minimizers to weighted least gradient problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Andres Zuniga","submitted_at":"2017-09-01T22:52:12Z","abstract_excerpt":"We revisit the question of existence and regularity of minimizers to weighted least gradient problems on a fixed bounded domain, subject to a Dirichlet boundary condition, in the case where the boundary data is continuous and the weight function is C^2 and bounded away from zero. Under suitable geometric conditions on the domain in R^n we construct continuous solutions of the above variational problem in any dimension n>=2, by extending the Sternberg-Williams-Ziemer technique to this setting of inhomogeneous variations. We show that the level sets of the constructed minimizer are minimal surfa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00502","kind":"arxiv","version":2},"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"}