SUFFICIENT CONDITIONS FOR THE EXISTENCE OF MINIMIZING HARMONIC MAPS WITH AXIAL SYMMETRY IN THE SMALL-AVERAGE REGIME

作     者：Di Fratta, Giovanni Slastikov, Valeriy V. Zarnescu, Arghir D. 

作者机构：Dipartimento di Matematica e Applicazioni "R. Caccioppoli" Università degli Studi di Napoli "Federico II" Via Cintia Napoli80126 Italy School of Mathematics University of Bristol BristolBS8 1TW United Kingdom BCAM Basque Center for Applied Mathematics Mazarredo 14 Bizkaia BilbaoE48009 Spain IKERBASQUE Basque Foundation for Science Maria Diaz de Haro 3 Bizkaia Bilbao48013 Spain Simion Stoilow Institute of Mathematics of the Romanian Academy P.O. Box 1-764 BucharestRO-014700 Romania 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2023年

核心收录：

主　　题：Computation theory 

摘      要：The paper concerns the analysis of global minimizers of a Dirichlet-type energy functional defined on the space of vector fields H1(S,T), where S and T are surfaces of revolution. The energy functional we consider is closely related to a reduced model in the variational theory of micromagnetism for the analysis of observable magnetization states in curved thin films. We show that axially symmetric minimizers always exist, and if the target surface T is never flat, then any coexisting minimizer must have line symmetry. Thus, the minimization problem reduces to the computation of an optimal one-dimensional profile. We also provide a necessary and sufficient condition for energy minimizers to be axially *** Codes 35A23, 35R45, 49R05, 49S05, 82D40 Copyright © 2023, The Authors. All rights reserved.