{"id":329,"date":"2016-06-17T06:35:56","date_gmt":"2016-06-17T06:35:56","guid":{"rendered":"http:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/?p=329"},"modified":"2016-06-17T06:35:56","modified_gmt":"2016-06-17T06:35:56","slug":"a-tour-of-lipschitz-truncations","status":"publish","type":"post","link":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/2016\/06\/17\/a-tour-of-lipschitz-truncations\/","title":{"rendered":"A tour of Lipschitz truncations"},"content":{"rendered":"<p><em>Bianca Stroffolini (Napoli, Italy)<\/em><\/p>\n<p>The purpose of the Lipschitz truncation is to regularize a given function by a Lipschitz continuous one by changing it only on a small \u00a0bad set. It is crucial for the applications that the function is not changed globally, which rules out the possibility of convolutions.<\/p>\n<p>The Lipschitz truncation technique was introduced by Acerbi-Fusco to show lower semicontinuity of certain variational integrals.<\/p>\n<p>Since then this technique has been successfully applied in many different areas: biting lemmas, existence theory \u00a0and regularity results of non-linear elliptic PDE . It was also successfully applied in the framework of non-Newtonian fluids of power law type and even in the context of numerical analysis.<\/p>\n<p>I will try to present some Lipschitz truncations Lemmas.<br \/>\nAs an application, existence\/ regularity of solutions of PDEs will be discussed.<\/p>\n<p><a href=\"http:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/programme\/\">Back to Programme<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bianca Stroffolini (Napoli, Italy) The purpose of the Lipschitz truncation is to regularize a given function by a Lipschitz continuous one by changing it only on a small \u00a0bad set. It is crucial for the applications that the function is not changed globally, which rules out the possibility of convolutions. The Lipschitz truncation technique was &hellip; <a href=\"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/2016\/06\/17\/a-tour-of-lipschitz-truncations\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">A tour of Lipschitz truncations<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"class_list":["post-329","post","type-post","status-publish","format-standard","hentry","category-abstracts"],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/posts\/329","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/users\/8"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/comments?post=329"}],"version-history":[{"count":0,"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/posts\/329\/revisions"}],"wp:attachment":[{"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/media?parent=329"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/categories?post=329"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/tags?post=329"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}