On the Hölder continuity for a class of vectorial problems-Reference-Cited by-同舟云学术

On the Hölder continuity for a class of vectorial problems

Published:2019-08-28 Issue:1 Volume:9 Page:1008-1025
ISSN:2191-950X
Container-title:Advances in Nonlinear Analysis
language:en
Short-container-title:

Author:

Cupini Giovanni¹,Focardi Matteo²,Leonetti Francesco³,Mascolo Elvira²

Affiliation:

1. Dipartimento di Matematica , Università di Bologna , Piazza di Porta S.Donato 5, 40126 , Bologna , Italy

2. Dipartimento di Matematica e Informatica “U. Dini” , Università di Firenze , Viale Morgagni 67/A, 50134 , Firenze , Italy

3. Dipartimento di Ingegneria e Scienze dell’Informazione e Matematica , Università di L’Aquila , Via Vetoio snc - Coppito, 67100 , L’Aquila , Italy

Abstract

Abstract In this paper we prove local Hölder continuity of vectorial local minimizers of special classes of integral functionals with rank-one and polyconvex integrands. The energy densities satisfy suitable structure assumptions and may have neither radial nor quasi-diagonal structure. The regularity of minimizers is obtained by proving that each component stays in a suitable De Giorgi class and, from this, we conclude about the Hölder continuity. In the final section, we provide some non-trivial applications of our results.

Publisher

Walter de Gruyter GmbH

Subject

Analysis

Reference23 articles.

1. E. De Giorgi, Sulla differenziabilità e l’analiticità delle estremali degli integrali multipli regolari, Mem. Accad. Sci. Torino. Cl. Sci. Fis. Mat. Nat. 3, (1957), 25–43.

2. M. Giaquinta and E. Giusti, On the regularity of minima of variational integrals, Acta Mathematica 148, (1983), 285–298.

3. E. De Giorgi, Un esempio di estremali discontinue per un problema variazionale di tipo ellittico, Boll. Un. Mat. Ital. (4) 1, (1968), 135–137.

4. J. Kristensen and G. Mingione, Sketches of regularity theory of the 20th century and the work of Jindrich Necas, in: Selected works of Jindrich Necas; pdes, continuum mechanics and regularity (S. Necasová, M. Pokorny, V. Sverák, Eds.) Birkhäuser, Basel, 2015.

5. C. Mooney and O. Savin, Some singular minimizers in low dimensions in the calculus of variations, Arch. Rational Mech. Anal. 221, (2016), 1–22.

Cited by 16 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. Remarks on the De Giorgi–Moser Techniques for Vectorial Problems;Differential Equations and Dynamical Systems;2024-03-20

2. An extension of De Giorgi class and applications;Journal of Functional Analysis;2024-03

3. О локальной непрерывности по Гeльдеру минимумов для одного класса интегральных функционалов вариационного исчисления;Функциональный анализ и его приложения;2024

4. Mathematical Analysis and Performance Evaluation of the GELU Activation Function in Deep Learning;Journal of Mathematics;2023-08-10

5. Not uniformly continuous densities and the local everywhere Hölder continuity of weak solutions of vectorial problems;Bollettino dell'Unione Matematica Italiana;2023-07-06