Sphere-valued harmonic maps with surface energy and the $K_{13}$ problem

Autor:	Stuart Day, Arghir Zarnescu
Jazyk:	angličtina
Rok vydání:	2016
Předmět:	Mathematics - Analysis of PDEs Applied Mathematics Romanian FOS: Mathematics Harmonic map language Regional science National authority Analysis language.human_language 76A15 58E20 49N60 Analysis of PDEs (math.AP) Mathematics
Zdroj:	BIRD: BCAM's Institutional Repository Data instname
Popis:	We consider an energy functional motivated by the celebrated K13 problem in the Oseen-Frank theory of nematic liquid crystals. It is defined for sphere-valued functions and appears as the usual Dirichlet energy with an additional surface term. It is known that this energy is unbounded from below and our aim has been to study the local minimizers. We show that even having a critical point in a suitable energy space imposes severe restrictions on the boundary conditions. Having suitable boundary conditions makes the energy functional bounded and in this case we study the partial regularity of the minimizers. Romanian National Authority for Scientific Research and Innovation, CNCSUEFISCDI, project number PN-II-RU-TE-2014-4-0657
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b2aab5e356172aa45742cb712f19ebb5 http://arxiv.org/abs/1607.01243 Zobrazit plný text záznamu