{"id":1998,"date":"2026-02-04T18:39:55","date_gmt":"2026-02-04T18:39:55","guid":{"rendered":"https:\/\/wp.math.berkeley.edu\/apde\/?p=1998"},"modified":"2026-02-04T18:39:55","modified_gmt":"2026-02-04T18:39:55","slug":"federico-franceschini-stanford","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/apde\/2026\/02\/04\/federico-franceschini-stanford\/","title":{"rendered":"Federico Franceschini (Stanford)"},"content":{"rendered":"<p>The APDE seminar on Monday, 2\/9, will be given by Federico Franceschini (Stanford) in-person in <strong>Evans 736,<\/strong>\u00a0and will also be broadcasted online via Zoom from\u00a0<strong>4:10pm to 5:00pm PST<\/strong>. To participate, please email Adam Black (adamblack<span id=\"eeb-322338-403021\"><span id=\"eeb-843318-171438\"><span id=\"eeb-203570-882396\"><span id=\"eeb-990440-551518\"><span id=\"eeb-688663-335757\"><span id=\"eeb-951702-73120\"><span id=\"eeb-183542-482341\"><span id=\"eeb-725178-862757\"><span id=\"eeb-367675-784580\">@berkeley.edu<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>).<\/p>\n<p><strong>Title<\/strong>: The dimension and behaviour of singularities of stable solutions to semilinear elliptic equations<\/p>\n<p><strong>Abstract: <\/strong>Let f(t) be a convex, positive, increasing nonlinearity. It is known that stable solutions of -\\Delta u =f(u) can be singular (i.e., unbounded) if the dimension n&gt;9.<\/p>\n<p>Brezis asked wether, if x=0 is such a singular point, then in general f'(u(x)) blows-up like ~|x|^{2-n}, as it happens in the model cases f(u)=u^p, f(u)=e^u.<\/p>\n<p>In this talk I will show the answer to this question and the interesting consequences it entails. This is a joint work with Alessio Figalli.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The APDE seminar on Monday, 2\/9, will be given by Federico Franceschini (Stanford) in-person in Evans 736,\u00a0and will also be broadcasted online via Zoom from\u00a04:10pm to 5:00pm PST. To participate, please email Adam Black (adamblack@berkeley.edu). Title: The dimension and behaviour of singularities of stable solutions to semilinear elliptic equations Abstract: Let f(t) be a convex, [&hellip;]<\/p>\n","protected":false},"author":119,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1998","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1998","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\/119"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/comments?post=1998"}],"version-history":[{"count":1,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1998\/revisions"}],"predecessor-version":[{"id":1999,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1998\/revisions\/1999"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/media?parent=1998"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/categories?post=1998"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/tags?post=1998"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}