We provide necessary and sufficient conditions for the uniqueness of minimisers of the Ginzburg-Landau functional for $\\RR^n$-valued maps under suitable convexity assumption on the potential and for $H^{1\/2} \\cap L^\\infty$ boundary data that is non-negative in a fixed direction $e\\in \\SSphere^{n-1}$. Furthermore, we show that, when minimisers are non-unique, the set of minimisers is invariant under appropriate orthogonal transformations of $\\RR^n$. As an application, we obtain symmetry results for minimisers corresponding to symmetric Dirichlet boundary data. We also prove corresponding results for harmonic maps. Joint work with R. Ignat, V. Slastikov and A. Zarnescu.<\/p>\n","protected":false},"excerpt":{"rendered":"
We provide necessary and sufficient conditions for the uniqueness of minimisers of the Ginzburg-Landau functional for $\\RR^n$-valued maps under suitable convexity assumption on the potential and for $H^{1\/2} \\cap L^\\infty$ boundary data that is non-negative in a fixed direction $e\\in \\SSphere^{n-1}$. Furthermore, we show that, when minimisers are non-unique, the set of minimisers is invariant\u2026 Read More »<\/a><\/span><\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2,4],"tags":[],"class_list":["post-377","post","type-post","status-publish","format-standard","hentry","category-abstracts","category-meeting-11"],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/posts\/377","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/comments?post=377"}],"version-history":[{"count":0,"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/posts\/377\/revisions"}],"wp:attachment":[{"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/media?parent=377"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/categories?post=377"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/tags?post=377"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}