{"id":501,"date":"2017-11-22T16:16:11","date_gmt":"2017-11-23T00:16:11","guid":{"rendered":"https:\/\/math.berkeley.edu\/wp\/apde\/?p=501"},"modified":"2017-11-22T16:16:11","modified_gmt":"2017-11-23T00:16:11","slug":"brian-krummel-uc-berkeley","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/apde\/2017\/11\/22\/brian-krummel-uc-berkeley\/","title":{"rendered":"Brian Krummel (UC Berkeley)"},"content":{"rendered":"<p>\t\t\t\tThe Analysis and PDE seminar will take place on Monday, November 27, from 4:10 to 5pm, in 740 Evans.<\/p>\n<p>Title: Fine properties of Dirichlet energy minimizing multi-valued functions<\/p>\n<p>Abstract: I will discuss the fine structure of the branch set of multivalued Dirichlet energy minimizing functions as developed by Almgren.  It is well-known that the dimension of the interior singular set of a Dirichlet energy minimizing function on an $n$-dimensional domain is at most $n-2$.  We show that the singular set is countably $(n-2)$-rectifiable and also prove the uniqueness of homogeneous tangent functions at almost every singular point.  Our approach involves adapting a \u201cblow up\u201d method due to Leon Simon, which was originally applied to multiplicity one classes of minimal submanifolds.  We apply Simon\u2019s method in the higher multiplicity setting of multivalued energy minimizers using techniques from prior work of Neshan Wickramasekera together with new estimates.  This is joint work with Neshan Wickramasekera.\t\t<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Analysis and PDE seminar will take place on Monday, November 27, from 4:10 to 5pm, in 740 Evans. Title: Fine properties of Dirichlet energy minimizing multi-valued functions Abstract: I will discuss the fine structure of the branch set of multivalued Dirichlet energy minimizing functions as developed by Almgren. It is well-known that the dimension [&hellip;]<\/p>\n","protected":false},"author":108,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-501","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/501","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/users\/108"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/comments?post=501"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/501\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/media?parent=501"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/categories?post=501"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/tags?post=501"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}