Calculus of Variations and Geometric Measure Theory

G. Cupini - M. Focardi - F. Leonetti - E. Mascolo

On the H\"older continuity for a class of vectorial problems

created by cupini on 19 Jun 2019
modified on 09 Sep 2019


Published Paper

Inserted: 19 jun 2019
Last Updated: 9 sep 2019

Journal: Adv. Nonlinear Anal.
Volume: 9
Pages: 1008-1025
Year: 2020


In this paper we prove local H\"older 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 H\"older continuity. In the final section, we provide some non-trivial applications of our results.

Keywords: regularity, minimizer, continuity, vectorial, H\"older, variational, integral