{"id":414,"date":"2024-07-05T09:14:33","date_gmt":"2024-07-05T07:14:33","guid":{"rendered":"https:\/\/mat.uab.cat\/web\/mprats\/?p=414"},"modified":"2025-11-24T09:50:58","modified_gmt":"2025-11-24T08:50:58","slug":"ignasi-guilles-mola-marti-prats-and-xavier-tolsa-the-dimension-of-planar-elliptic-measures-arising-from-lipschitz-matrices-in-reifenberg-flat-domains","status":"publish","type":"post","link":"https:\/\/mat.uab.cat\/web\/mprats\/2024\/07\/05\/ignasi-guilles-mola-marti-prats-and-xavier-tolsa-the-dimension-of-planar-elliptic-measures-arising-from-lipschitz-matrices-in-reifenberg-flat-domains\/","title":{"rendered":"Ignasi Guill\u00e9s-Mola, Mart\u00ed Prats and Xavier Tolsa: The dimension of planar elliptic measures arising from Lipschitz matrices in Reifenberg flat domains"},"content":{"rendered":"\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\/10.48550\/arXiv.2406.11604\" target=\"_blank\" rel=\"noreferrer noopener\">arXiv<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/doi.org\/10.1007\/s13324-025-01067-5\" target=\"_blank\" rel=\"noreferrer noopener\">AAMP<\/a><\/div>\n<\/div>\n\n\n\n<p>In this paper we show that, given a planar Reifenberg flat domain with small constant and a divergence form operator associated to a real (not necessarily symmetric) uniformly elliptic matrix with Lipschitz coefficients, the Hausdorff dimension of its elliptic measure is at most 1. More precisely, we prove that there exists a subset of the boundary with full elliptic measure and with \u03c3-finite one-dimensional Hausdorff measure. For Reifenberg flat domains, this result extends a previous work of Thomas H. Wolff for the harmonic measure.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In this paper we show that, given a planar Reifenberg flat domain with small constant and a divergence form operator associated to a real (not necessarily symmetric) uniformly elliptic matrix with Lipschitz coefficients, the Hausdorff dimension of its elliptic measure is at most 1. More precisely, we prove that there exists a subset of the &hellip; <a href=\"https:\/\/mat.uab.cat\/web\/mprats\/2024\/07\/05\/ignasi-guilles-mola-marti-prats-and-xavier-tolsa-the-dimension-of-planar-elliptic-measures-arising-from-lipschitz-matrices-in-reifenberg-flat-domains\/\" class=\"more-link\">Continua la lectura de <span class=\"screen-reader-text\">Ignasi Guill\u00e9s-Mola, Mart\u00ed Prats and Xavier Tolsa: The dimension of planar elliptic measures arising from Lipschitz matrices in Reifenberg flat 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-414","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\/414","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=414"}],"version-history":[{"count":4,"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/posts\/414\/revisions"}],"predecessor-version":[{"id":499,"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/posts\/414\/revisions\/499"}],"wp:attachment":[{"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/media?parent=414"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/categories?post=414"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/tags?post=414"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}