{"id":432,"date":"2022-10-06T12:08:02","date_gmt":"2022-10-06T11:08:02","guid":{"rendered":"https:\/\/research.reading.ac.uk\/pure-and-applied-analysis\/?p=432"},"modified":"2022-10-06T12:08:02","modified_gmt":"2022-10-06T11:08:02","slug":"isosupremic-vectorial-minimisation-problems-in-linfty-with-general-nonlinear-constraints","status":"publish","type":"post","link":"https:\/\/research.reading.ac.uk\/pure-and-applied-analysis\/isosupremic-vectorial-minimisation-problems-in-linfty-with-general-nonlinear-constraints\/","title":{"rendered":"Isosupremic vectorial minimisation problems in $L^\\infty$ with general nonlinear constraints"},"content":{"rendered":"<p><strong>Friday 4 March, 12:00 \u2013 13:00, M113<\/strong><\/p>\n<p>In this talk we discuss minimisation problems in $L^\\infty$ for general quasiconvex first order functionals, where the class of admissible mappings is constrained by the sublevel sets of another supremal functional and by the zero set of a nonlinear operator. Via the method of $L^p$ approximations as $p\\to \\infty$, we illustrate the existence of constrained minimisers in $L^p$ for all large $p&lt; \\infty$, which in turn converge to a desired $L^\\infty$ minimiser as $p\\to \\infty$. We further show that the special $L^\\infty$ minimiser we construct solves a divergence PDE system which involves certain auxiliary measures as coefficients. This can be seen as a divergence form counterpart of the Aronsson-Euler PDE system which is associated with the $L^\\infty$ constrained minimisation problem. This talk is based on joint work with Nikos Katzourakis.<\/p>\n<p><strong>Ed Clark (PhD student)<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Friday 4 March, 12:00 \u2013 13:00, M113 In this talk we discuss minimisation problems in $L^\\infty$ for general quasiconvex first order functionals, where the class of admissible mappings is constrained&#8230;<a class=\"read-more\" href=\"&#104;&#116;&#116;&#112;&#115;&#58;&#47;&#47;&#114;&#101;&#115;&#101;&#97;&#114;&#99;&#104;&#46;&#114;&#101;&#97;&#100;&#105;&#110;&#103;&#46;&#97;&#99;&#46;&#117;&#107;&#47;&#112;&#117;&#114;&#101;&#45;&#97;&#110;&#100;&#45;&#97;&#112;&#112;&#108;&#105;&#101;&#100;&#45;&#97;&#110;&#97;&#108;&#121;&#115;&#105;&#115;&#47;&#105;&#115;&#111;&#115;&#117;&#112;&#114;&#101;&#109;&#105;&#99;&#45;&#118;&#101;&#99;&#116;&#111;&#114;&#105;&#97;&#108;&#45;&#109;&#105;&#110;&#105;&#109;&#105;&#115;&#97;&#116;&#105;&#111;&#110;&#45;&#112;&#114;&#111;&#98;&#108;&#101;&#109;&#115;&#45;&#105;&#110;&#45;&#108;&#105;&#110;&#102;&#116;&#121;&#45;&#119;&#105;&#116;&#104;&#45;&#103;&#101;&#110;&#101;&#114;&#97;&#108;&#45;&#110;&#111;&#110;&#108;&#105;&#110;&#101;&#97;&#114;&#45;&#99;&#111;&#110;&#115;&#116;&#114;&#97;&#105;&#110;&#116;&#115;&#47;\">Read More ><\/a><\/p>\n","protected":false},"author":219,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"__cvm_playback_settings":[],"__cvm_video_id":"","footnotes":""},"categories":[14],"tags":[16,18],"coauthors":[12],"class_list":["post-432","post","type-post","status-publish","format-standard","hentry","category-events","tag-analysis-seminar","tag-spring-2022"],"acf":[],"aioseo_notices":[],"cc_featured_image_caption":{"caption_text":"","source_text":"","source_url":""},"_links":{"self":[{"href":"https:\/\/research.reading.ac.uk\/pure-and-applied-analysis\/wp-json\/wp\/v2\/posts\/432","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/research.reading.ac.uk\/pure-and-applied-analysis\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/research.reading.ac.uk\/pure-and-applied-analysis\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/research.reading.ac.uk\/pure-and-applied-analysis\/wp-json\/wp\/v2\/users\/219"}],"replies":[{"embeddable":true,"href":"https:\/\/research.reading.ac.uk\/pure-and-applied-analysis\/wp-json\/wp\/v2\/comments?post=432"}],"version-history":[{"count":1,"href":"https:\/\/research.reading.ac.uk\/pure-and-applied-analysis\/wp-json\/wp\/v2\/posts\/432\/revisions"}],"predecessor-version":[{"id":433,"href":"https:\/\/research.reading.ac.uk\/pure-and-applied-analysis\/wp-json\/wp\/v2\/posts\/432\/revisions\/433"}],"wp:attachment":[{"href":"https:\/\/research.reading.ac.uk\/pure-and-applied-analysis\/wp-json\/wp\/v2\/media?parent=432"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/research.reading.ac.uk\/pure-and-applied-analysis\/wp-json\/wp\/v2\/categories?post=432"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/research.reading.ac.uk\/pure-and-applied-analysis\/wp-json\/wp\/v2\/tags?post=432"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/research.reading.ac.uk\/pure-and-applied-analysis\/wp-json\/wp\/v2\/coauthors?post=432"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}