{"id":5208,"date":"2023-03-31T07:30:35","date_gmt":"2023-03-31T07:30:35","guid":{"rendered":"https:\/\/iamm.in.ua\/?p=5208"},"modified":"2023-04-27T08:03:14","modified_gmt":"2023-04-27T08:03:14","slug":"seminar-contemporary-analysis-and-partial-differential-equations-20-04-2023","status":"publish","type":"post","link":"https:\/\/iamm.in.ua\/?p=5208&lang=en","title":{"rendered":"SEMINAR \u201cContemporary Analysis and Partial Differential Equations\u201d (20.04.2023)"},"content":{"rendered":"<p><script src=\"https:\/\/polyfill.io\/v3\/polyfill.min.js?features=es6\"><\/script><br \/>\n<script id=\"MathJax-script\" src=\"https:\/\/cdn.jsdelivr.net\/npm\/mathjax@3\/es5\/tex-mml-chtml.js\" async=\"\"><\/script><br \/>\n<span style=\"font-family: georgia, palatino, serif; font-size: 14pt;\"><img decoding=\"async\" loading=\"lazy\" class=\"size-medium wp-image-4770 alignright\" src=\"https:\/\/iamm.in.ua\/wp-content\/uploads\/2023\/01\/Allea-300x84.jpg\" alt=\"\" width=\"300\" height=\"84\" srcset=\"https:\/\/iamm.in.ua\/wp-content\/uploads\/2023\/01\/Allea-300x84.jpg 300w, https:\/\/iamm.in.ua\/wp-content\/uploads\/2023\/01\/Allea.jpg 483w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"font-family: georgia, palatino, serif; font-size: 14pt;\"><strong><img decoding=\"async\" loading=\"lazy\" class=\"wp-image-4773 alignleft\" src=\"https:\/\/iamm.in.ua\/wp-content\/uploads\/2023\/01\/Logo-IAMM-300x292.png\" alt=\"\" width=\"133\" height=\"129\" srcset=\"https:\/\/iamm.in.ua\/wp-content\/uploads\/2023\/01\/Logo-IAMM-300x292.png 300w, https:\/\/iamm.in.ua\/wp-content\/uploads\/2023\/01\/Logo-IAMM.png 583w\" sizes=\"(max-width: 133px) 100vw, 133px\" \/><\/strong><\/span><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/orcid.org\/0000-0001-7065-4163\" target=\"_blank\" rel=\"noopener\"><span style=\"font-family: georgia, palatino, serif; font-size: 14pt;\"><strong>Simone Ciani<\/strong><\/span><\/a><\/p>\n<p style=\"text-align: center;\"><span style=\"font-family: georgia, palatino, serif; font-size: 14pt;\">University of Bolonga, Italy<\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"font-size: 14pt; font-family: georgia, palatino, serif;\">simone.ciani3@unibo.it<\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"font-family: georgia, palatino, serif; font-size: 14pt;\"><strong><em>Anisotropic De Giorgi Classes and the Regularity of Solutions to Some Anisotropic Elliptic Equations<\/em><\/strong><\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"font-family: georgia, palatino, serif; font-size: 14pt;\">Thursday, 20 April 2023 at 15:00<\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"font-family: georgia, palatino, serif; font-size: 14pt;\">On line:&nbsp;<a href=\"https:\/\/meet.google.com\/mna-fdrh-tcm\">https:\/\/meet.google.com\/mna-fdrh-tcm<\/a><\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"font-family: georgia, palatino, serif; font-size: 14pt;\"><strong>Abstract<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; font-size: 14pt;\">We introduce anisotropic De Giorgi classes through general energy inequalities, to describe an old problem that remained open. We motivate the introduction of such classes by recent results on solutions to anisotropic singular equations of the kind<\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif; font-size: 14pt;\">$$ \\sum^{s}_{i=1} \\partial_{ii} u + \\sum^{N}_{i=s+1} \\partial_{i} \\left( A_{i} (x, u, \\nabla u)\\right) = 0, \\quad x\\in\\Omega\\subset\\subset \\mathbb{R}^{N} \\text{ for } 1\\ge s \\ge (N-1)$$<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; font-size: 14pt;\">where each operator \\(A_{i}\\) behaves as the \\(p\\)-Laplacian with \\(1 \\lt p \\lt 2\\). The resolution of this special problem borrows parabolic potential techniques of expansion of positivity to obtain the interior H\u00f6lder continuity and some integral and pointwise Harnack inequalities.<\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif; font-size: 14pt;\">Seminar video report<\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif; font-size: 14pt;\"> <iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/OEzy8EkG0qQ\" width=\"560\" height=\"314\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<div class=\"slide-text-bg2\"><span>&nbsp; &nbsp; &nbsp; &nbsp; Simone Ciani University of Bolonga, Italy simone.ciani3@unibo.it Anisotropic De Giorgi Classes and the Regularity of Solutions <\/span><\/div>\n<div class=\"slide-btn-area-sm\"><a href=\"https:\/\/iamm.in.ua\/?p=5208&#038;lang=en\" class=\"slide-btn-sm\">\u041f\u0440\u043e\u0447\u0438\u0442\u0430\u0442\u044c \u0431\u043e\u043b\u044c\u0448\u0435<\/a><\/div>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[99,74],"tags":[],"_links":{"self":[{"href":"https:\/\/iamm.in.ua\/index.php?rest_route=\/wp\/v2\/posts\/5208"}],"collection":[{"href":"https:\/\/iamm.in.ua\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/iamm.in.ua\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/iamm.in.ua\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/iamm.in.ua\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5208"}],"version-history":[{"count":4,"href":"https:\/\/iamm.in.ua\/index.php?rest_route=\/wp\/v2\/posts\/5208\/revisions"}],"predecessor-version":[{"id":5386,"href":"https:\/\/iamm.in.ua\/index.php?rest_route=\/wp\/v2\/posts\/5208\/revisions\/5386"}],"wp:attachment":[{"href":"https:\/\/iamm.in.ua\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5208"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/iamm.in.ua\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5208"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/iamm.in.ua\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5208"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}