{"id":53,"date":"2019-10-05T13:07:32","date_gmt":"2019-10-05T11:07:32","guid":{"rendered":"https:\/\/mat.uab.cat\/web\/mprats\/?p=53"},"modified":"2025-07-09T15:25:52","modified_gmt":"2025-07-09T13:25:52","slug":"marti-prats-sobolev-regularity-of-quasiconformal-mappings-on-domains","status":"publish","type":"post","link":"https:\/\/mat.uab.cat\/web\/mprats\/2019\/10\/05\/marti-prats-sobolev-regularity-of-quasiconformal-mappings-on-domains\/","title":{"rendered":"Mart\u00ed Prats: Sobolev regularity of quasiconformal mappings on domains"},"content":{"rendered":"\n<div class=\"wp-block-group is-content-justification-left is-nowrap is-layout-flex wp-container-core-group-is-layout-f56a869c wp-block-group-is-layout-flex\">\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/arxiv.org\/abs\/1507.04332\" target=\"_blank\" rel=\"noreferrer noopener\">arXiv<\/a><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/doi.org\/10.1007\/s11854-019-0031-9\" target=\"_blank\" rel=\"noreferrer noopener\">J. Anal. Math.<\/a><\/div>\n<\/div>\n<\/div>\n\n\n\n\n\n\n\n<p>Consider a Lipschitz domain \\( \\Omega \\) and a measurable function \\( \\mu \\) supported in \\( \\overline\\Omega \\) with \\( \\left\\|{\\mu}\\right\\|_{L^\\infty}&lt; 1 \\). Then the derivatives of a quasiconformal solution of the Beltrami equation \\( \\overline{\\partial} f =\\mu\\, \\partial f \\) inherit the Sobolev regularity \\( W^{n,p}(\\Omega) \\) of the Beltrami coefficient \\( \\mu \\) as long as \\( \\Omega \\) is regular enough. The condition obtained is that the outward unit normal vector \\( N \\) of the boundary of the domain is in the trace space, that is, \\( N\\in B^{n-1\/p}_{p,p}(\\partial\\Omega) \\).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Consider a Lipschitz domain \\( \\Omega \\) and a measurable function \\( \\mu \\) supported in \\( \\overline\\Omega \\) with \\( \\left\\|{\\mu}\\right\\|_{L^\\infty}&lt; 1 \\). Then the derivatives of a quasiconformal solution of the Beltrami equation \\( \\overline{\\partial} f =\\mu\\, \\partial f \\) inherit the Sobolev regularity \\( W^{n,p}(\\Omega) \\) of the Beltrami coefficient \\( \\mu &hellip; <a href=\"https:\/\/mat.uab.cat\/web\/mprats\/2019\/10\/05\/marti-prats-sobolev-regularity-of-quasiconformal-mappings-on-domains\/\" class=\"more-link\">Continua la lectura de <span class=\"screen-reader-text\">Mart\u00ed Prats: Sobolev regularity of quasiconformal mappings on domains<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":53,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[95],"tags":[39],"class_list":["post-53","post","type-post","status-publish","format-standard","hentry","category-papers-en","tag-papers-en"],"_links":{"self":[{"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/posts\/53","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/users\/53"}],"replies":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/comments?post=53"}],"version-history":[{"count":7,"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/posts\/53\/revisions"}],"predecessor-version":[{"id":453,"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/posts\/53\/revisions\/453"}],"wp:attachment":[{"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/media?parent=53"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/categories?post=53"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/tags?post=53"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}