{"paper":{"title":"Dirichlet/Neumann problems and Hardy classes for the planar conductivity equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Juliette Leblond, Laurent Baratchart, Yannick Fischer","submitted_at":"2011-11-29T11:53:40Z","abstract_excerpt":"We study Hardy spaces $H^p_\\nu$ of the conjugate Beltrami equation $\\bar{\\partial} f=\\nu\\bar{\\partial f}$ over Dini-smooth finitely connected domains, for real contractive $\\nu\\in W^{1,r}$ with $r>2$, in the range $r/(r-1)<p<\\infty$. We develop a theory of conjugate functions and apply it to solve Dirichlet and Neumann problems for the conductivity equation $\\nabla.(\\sigma \\nabla u)=0$ where $\\sigma=(1-\\nu)/(1+\\nu)$. In particular situations, we also consider some density properties of traces of solutions together with boundary approximation issues."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6776","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"}