{"id":181,"date":"2016-10-03T14:37:29","date_gmt":"2016-10-03T14:37:29","guid":{"rendered":"http:\/\/sites.maths.cf.ac.uk\/swngsn\/?p=181"},"modified":"2016-10-03T14:37:29","modified_gmt":"2016-10-03T14:37:29","slug":"a-theory-of-lower-semicontinuity-for-integral-functionals-with-linear-growth-and-u-dependence-giles-shaw-reading-cambridge","status":"publish","type":"post","link":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/2016\/10\/03\/a-theory-of-lower-semicontinuity-for-integral-functionals-with-linear-growth-and-u-dependence-giles-shaw-reading-cambridge\/","title":{"rendered":"A theory of Lower Semicontinuity for Integral Functionals with Linear Growth and u-dependence, Giles Shaw (Reading &amp; Cambridge)"},"content":{"rendered":"<div class=\"page\" title=\"Page 1\">\n<div class=\"layoutArea\">\n<div class=\"column\">\n<p>Variational problems with linear growth arise naturally in the Calcu- lus of Variations from the study of singular perturbation problems associated to a large number of physical and mathematical applications. These problems must be posed over the class of functions of bounded variation, and their analysis is signifi- cantly more involved than that which is required for variational problems posed over Sobolev spaces. I will discuss my progress with Filip Rindler towards developing a general, robust, theory to study the lower semicontinuity properties of this class of problems. Our approach involves associating a class of measures to the graphs of BV functions before constructing a family of Young measures to characterise their limiting behaviour. On a technical level, we make use of fine properties of BV functions as well as methods from geometric measure theory.<\/p>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Variational problems with linear growth arise naturally in the Calcu- lus of Variations from the study of singular perturbation problems associated to a large number of physical and mathematical applications. These problems must be posed over the class of functions of bounded variation, and their analysis is signifi- cantly more involved than that which is\u2026 <span class=\"read-more\"><a href=\"https:\/\/sites.maths.cf.ac.uk\/swngsn\/2016\/10\/03\/a-theory-of-lower-semicontinuity-for-integral-functionals-with-linear-growth-and-u-dependence-giles-shaw-reading-cambridge\/\">Read More &raquo;<\/a><\/span><\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2,5],"tags":[],"class_list":["post-181","post","type-post","status-publish","format-standard","hentry","category-abstracts","category-meeting-4"],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/posts\/181","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/comments?post=181"}],"version-history":[{"count":0,"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/posts\/181\/revisions"}],"wp:attachment":[{"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/media?parent=181"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/categories?post=181"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/tags?post=181"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}