{"id":8139,"date":"2023-03-05T12:52:11","date_gmt":"2023-03-05T11:52:11","guid":{"rendered":"https:\/\/www.dm.unipi.it\/?post_type=unipievents&#038;p=8139"},"modified":"2023-03-05T12:52:14","modified_gmt":"2023-03-05T11:52:14","slug":"optimal-regularity-for-supercritical-parabolic-obstacle-problems","status":"publish","type":"unipievents","link":"https:\/\/www.dm.unipi.it\/en\/eventi\/optimal-regularity-for-supercritical-parabolic-obstacle-problems\/","title":{"rendered":"Optimal regularity for supercritical parabolic obstacle problems &ndash; Dami\u00e0 Torres (Universitat de Barcelona)"},"content":{"rendered":"\n<p>The parabolic nonlocal obstacle problem is said to be in the supercritical regime (s &lt; 1\/2) when the time derivative is of higher order than the diffusion&nbsp;operator. We will discuss the optimal $C^{1,1}$ regularity of solutions and the $C^{1,\u03b1}$ regularity of the free boundary. The arguments rely on comparison principles and the scaling of the equation to circumvent the fact that blow-ups, the usual technique for free boundary problems, are not useful in this context.<\/p>\n\n\n\n<p>This is a joint work with X. Ros-Oton.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The parabolic nonlocal obstacle problem is said to be in the supercritical regime (s &lt; 1\/2) when the time derivative&hellip;<\/p>\n<p><a class=\"btn btn-dark btn-sm unipi-read-more-link\" href=\"https:\/\/www.dm.unipi.it\/en\/eventi\/optimal-regularity-for-supercritical-parabolic-obstacle-problems\/\">Read More&#8230;<\/a><\/p>\n","protected":false},"author":55,"featured_media":0,"template":"","tags":[],"unipievents_taxonomy":[],"class_list":["post-8139","unipievents","type-unipievents","status-publish","hentry"],"acf":[],"unipievents_startdate":1678298400,"unipievents_enddate":1678302000,"unipievents_place":"Aula Magna","unipievents_externalid":0,"jetpack_sharing_enabled":true,"publishpress_future_workflow_manual_trigger":{"enabledWorkflows":[]},"_links":{"self":[{"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/unipievents\/8139","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/unipievents"}],"about":[{"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/types\/unipievents"}],"author":[{"embeddable":true,"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/users\/55"}],"version-history":[{"count":3,"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/unipievents\/8139\/revisions"}],"predecessor-version":[{"id":8371,"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/unipievents\/8139\/revisions\/8371"}],"wp:attachment":[{"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/media?parent=8139"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/tags?post=8139"},{"taxonomy":"unipievents_taxonomy","embeddable":true,"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/unipievents_taxonomy?post=8139"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}