Everywhere Holder continuity of vectorial local minimizers of special classes of integral functionals with rank one integrands

In this paper we study the everywhere Holder continuity of theminima of the following class of vectorial integral functionals integral(Omega) Sigma(n)(alpha=1) f(alpha)(x, u(alpha), del u(alpha)) + G (x, u, del u) dx 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 Holder continuity.

Automated summary

This paper studies the everywhere Holder continuity of the minima of a class of vectorial integral functionals. By analyzing the properties of each component, the regularity of the minima and the Holder continuity are obtained.