On the Hölder continuity for a class of vectorial problems

Advances in Nonlinear Analysis

article

Giovanni Cupini¹  Matteo Focardi²  Francesco Leonetti³  Elvira Mascolo² 

[1] Dipartimento di Matematica, Università di Bologna;Dipartimento di Matematica e Informatica “U. Dini”, Università di Firenze;Dipartimento di Ingegneria e Scienze dell’Informazione e Matematica, Università di L’Aquila

关键词: Holder;    continuity;    regularity;    vectorial;    minimizer;    variational;    integral;   

DOI  :  10.1515/anona-2020-0039

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

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.

【 授权许可】

CC BY