{"paper":{"title":"Geometric regularity for elliptic equations in double-divergence form","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Edgard A. Pimentel, Makson S. Santos, Raimundo Leit\\~ao","submitted_at":"2019-04-18T15:56:45Z","abstract_excerpt":"In this paper, we examine the regularity of the solutions to the double-divergence equation. We establish improved H\\\"older continuity as solutions approach their zero level-sets. In fact, we prove that $\\alpha$-H\\\"older continuous coefficients lead to solutions of class $\\mathcal{C}^{1^-}$, locally. Under the assumption of Sobolev differentiable coefficients, we establish regularity in the class $\\mathcal{C}^{1,1^-}$. Our results unveil improved continuity along a nonphysical free boundary, where the weak formulation of the problem vanishes. We argue through a geometric set of techniques, imp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.08856","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"}