{"id":76,"date":"2018-10-05T14:14:47","date_gmt":"2018-10-05T12:14:47","guid":{"rendered":"https:\/\/mat.uab.cat\/web\/mprats\/?p=76"},"modified":"2025-07-09T15:28:12","modified_gmt":"2025-07-09T13:28:12","slug":"marti-prats-beltrami-equations-in-the-plane-and-sobolev-regularity","status":"publish","type":"post","link":"https:\/\/mat.uab.cat\/web\/mprats\/2018\/10\/05\/marti-prats-beltrami-equations-in-the-plane-and-sobolev-regularity\/","title":{"rendered":"Mart\u00ed Prats: Beltrami equations in the plane and Sobolev regularity"},"content":{"rendered":"\n<div class=\"wp-block-group is-nowrap is-layout-flex wp-container-core-group-is-layout-ad2f72ca 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\/1606.07751\" 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\/10.3934\/cpaa.2018018\" target=\"_blank\" rel=\"noreferrer noopener\">Commun. Pur. Appl. Anal.<\/a><\/div>\n<\/div>\n<\/div>\n\n\n\n\n\n\n\n<p>Some new results regarding the Sobolev regularity of the principal solution of the linear Beltrami equation \\(\\bar\\partial f = \\mu \\partial f + \\nu\\, \\overline{\\partial f}\\) for discontinuous Beltrami coefficients \\(\\mu\\) and \\(\\nu\\) are obtained, using Kato-Ponce commutators. A conjecture on the cases where the limitations of the method do not work is raised.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Some new results regarding the Sobolev regularity of the principal solution of the linear Beltrami equation \\(\\bar\\partial f = \\mu \\partial f + \\nu\\, \\overline{\\partial f}\\) for discontinuous Beltrami coefficients \\(\\mu\\) and \\(\\nu\\) are obtained, using Kato-Ponce commutators. A conjecture on the cases where the limitations of the method do not work is raised.<\/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-76","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\/76","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=76"}],"version-history":[{"count":8,"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/posts\/76\/revisions"}],"predecessor-version":[{"id":456,"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/posts\/76\/revisions\/456"}],"wp:attachment":[{"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/media?parent=76"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/categories?post=76"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/tags?post=76"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}