{"paper":{"title":"Regularity of solutions to time-harmonic Maxwell's system with various lower than Lipschitz coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Basang Tsering-Xiao, Wei Xiang","submitted_at":"2016-03-07T02:51:21Z","abstract_excerpt":"In this paper, we study the regularity of the solutions of Maxwell's equations in a bounded domain. We consider several different types of low regularity assumptions to the coefficients which are all less than Lipschitz. We first develop a new approach by giving $\\mathcal{H}^1$ estimate when the coefficients are $\\mathcal{L}^{\\infty}$ bounded; and then we derive $\\mathcal{W}^{1,p}$ estimates for every $p > 2$ when one of the leading coefficients is simply continuous; Finally, we extend the result to $\\mathcal{C}^{1,\\alpha}$ almost everywhere for the solution of the homogeneous Maxwell's equati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01922","kind":"arxiv","version":3},"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"}