{"id":2022,"date":"2026-04-17T06:41:02","date_gmt":"2026-04-17T06:41:02","guid":{"rendered":"https:\/\/wp.math.berkeley.edu\/apde\/?p=2022"},"modified":"2026-04-17T06:41:02","modified_gmt":"2026-04-17T06:41:02","slug":"josef-greilhuber-stanford","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/apde\/2026\/04\/17\/josef-greilhuber-stanford\/","title":{"rendered":"Josef Greilhuber (Stanford)"},"content":{"rendered":"<p>The APDE seminar on Monday, 4\/20, will be given by Josef Greilhuber (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>: Non-density of nodal lines in the clamped plate problem<\/p>\n<p><strong>Abstract: <\/strong>It is well known that the nodal set (i.e., zero set) of an eigenfunction of the Laplacian \u2013 modelling a fundamental mode of vibration of an elastic membrane \u2013 is dense at the scale of its characteristic wave-length.<u><\/u><u><\/u><\/p>\n<p>In contrast, we show that the nodal set of high energy eigenfunctions of the clamped plate problem \u2013 a fourth order PDE modeling a vibrating metal plate \u2013 is not necessarily dense and can in fact exhibit macroscopic \u201cnodal voids\u201d.<u><\/u><u><\/u><\/p>\n<p>Specifically, we construct small deformations of the unit disk admitting a clamped plate eigenfunction of arbitrarily high frequency that does not vanish in a disk of radius ~0.44.<u><\/u><u><\/u><\/p>\n<p>Remarkably, this radius is sharp, simultaneously providing the asymptotic upper bound for the size of such circular nodal voids among small perturbations of the disk.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The APDE seminar on Monday, 4\/20, will be given by Josef Greilhuber (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: Non-density of nodal lines in the clamped plate problem Abstract: It is well known that the nodal set (i.e., [&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-2022","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/2022","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=2022"}],"version-history":[{"count":1,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/2022\/revisions"}],"predecessor-version":[{"id":2023,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/2022\/revisions\/2023"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/media?parent=2022"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/categories?post=2022"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/tags?post=2022"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}