{"paper":{"title":"Regularity theory for solutions to second order elliptic operators with complex coefficients and the $L^p$ Dirichlet problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jill Pipher, Martin Dindo\\v{s}","submitted_at":"2016-12-05T21:45:25Z","abstract_excerpt":"We establish a new theory of regularity for elliptic complex valued second order equations of the form $\\mathcal L=$div$A(\\nabla\\cdot)$, when the coefficients of the matrix $A$ satisfy a natural algebraic condition, a strengthened version of a condition known in the literature as $L^p$-dissipativity. Precisely, the regularity result is a reverse H\\\"older condition for $L^p$ averages of solutions on interior balls, and serves as a replacement for the De Giorgi - Nash - Moser regularity of solutions to real-valued divergence form elliptic operators. In a series of papers, Cialdea and Maz'ya stud"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01568","kind":"arxiv","version":4},"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"}