On symmetry of energy minimizing harmonic-type maps on cylindrical surfaces

Author:

Fratta Giovanni Di1,Fiorenza Alberto23,Slastikov Valeriy4

Affiliation:

1. Dipartimento di Matematica e Applicazioni "R. Caccioppoli", Università degli Studi di Napoli "Federico Ⅱ", Via Cintia, Complesso Monte S. Angelo, 80126 Napoli, Italy

2. Dipartimento di Architettura, Università di Napoli Federico Ⅱ, Via Monteoliveto, 3, I-80134 Napoli, Italy

3. Istituto per le Applicazioni del Calcolo "Mauro Picone", sezione di Napoli, Consiglio Nazionale delle Ricerche, via Pietro Castellino, 111, I-80131 Napoli, Italy

4. School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom

Abstract

<abstract><p>The paper concerns the analysis of global minimizers of a Dirichlet-type energy functional in the class of $ \mathbb{S}^2 $-valued maps defined in cylindrical surfaces. The model naturally arises as a curved thin-film limit in the theories of nematic liquid crystals and micromagnetics. We show that minimal configurations are $ z $-invariant and that energy minimizers in the class of weakly axially symmetric competitors are, in fact, axially symmetric. Our main result is a family of <italic>sharp</italic> Poincaré-type inequality on the circular cylinder, which allows for establishing a nearly complete picture of the energy landscape. The presence of symmetry-breaking phenomena is highlighted and discussed. Finally, we provide a complete characterization of in-plane minimizers, which typically appear in numerical simulations for reasons we explain.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Mathematical Physics,Analysis

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Sufficient conditions for the existence of minimizing harmonic maps with axial symmetry in the small-average regime;Nonlinear Analysis: Real World Applications;2024-08

2. Reduced energies for thin ferromagnetic films with perpendicular anisotropy;Mathematical Models and Methods in Applied Sciences;2024-07-30

3. A modular Poincaré–Wirtinger inequality for Sobolev spaces with variable exponents;Nonlinear Differential Equations and Applications NoDEA;2024-06-21

4. The mathematics of thin structures;Quarterly of Applied Mathematics;2022-09-01

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