On the Hölder continuity for a class of vectorial problems

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.

Keywords

• holder
• continuity
• regularity
• vectorial
• minimizer
• variational
• integral
• primary: 49n60
• secondary: 35j50