Inserted: 19 jun 2019
Last Updated: 9 sep 2019
Journal: Adv. Nonlinear Anal.
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