{"id":374,"date":"2016-06-17T07:08:33","date_gmt":"2016-06-17T07:08:33","guid":{"rendered":"http:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/?p=374"},"modified":"2016-06-17T07:08:33","modified_gmt":"2016-06-17T07:08:33","slug":"liquid-drops-on-a-rough-surface","status":"publish","type":"post","link":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/2016\/06\/17\/liquid-drops-on-a-rough-surface\/","title":{"rendered":"Some results on stochastic homogenization of non-convex Hamilton-Jacobi equations"},"content":{"rendered":"<p><em>William Feldman (Chicago, USA)<\/em><\/p>\n<p>I will discuss some progress about the homogenization of non-convex Hamilton-Jacobi equations in random media.\u00a0 I will revisit the recent counter-example of Ziliotto who constructed a coercive but non-convex Hamilton-Jacobi equation with stationary ergodic random potential field for which homogenization does not hold.\u00a0 We have extended this result showing that for any Hamiltonian with a strict saddle-point there is a random stationary ergodic potential field V so that homogenization does not hold for the Hamiltonian H = h(p)-V(x).\u00a0 I will also discuss a positive result, \u00a0under a finite range of dependence assumption we show that homogenization holds for Hamiltonians with strictly star-shaped sub-level sets.<\/p>\n<p>This talk is based on joint work with P. Souganidis.<\/p>\n<p><a href=\"http:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/programme\/\">Back to Programme<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>William Feldman (Chicago, USA) I will discuss some progress about the homogenization of non-convex Hamilton-Jacobi equations in random media.\u00a0 I will revisit the recent counter-example of Ziliotto who constructed a coercive but non-convex Hamilton-Jacobi equation with stationary ergodic random potential field for which homogenization does not hold.\u00a0 We have extended this result showing that for &hellip; <a href=\"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/2016\/06\/17\/liquid-drops-on-a-rough-surface\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Some results on stochastic homogenization of non-convex Hamilton-Jacobi equations<\/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-374","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\/374","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=374"}],"version-history":[{"count":0,"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/posts\/374\/revisions"}],"wp:attachment":[{"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/media?parent=374"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/categories?post=374"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/tags?post=374"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}