Boundary regularity of Dirichlet minimizing Q-valued functions

Abstract

We consider the H\older continuity for the Dirichlet problem at the boundary. Almgren introduced the multivalued; Q-valued functions for studying regularity of minimal surfaces in higher codimension. The H\older continuity in the interior for Dirichlet minimizers is an outcome of Almgren's original theory, to which C. De Lellis and E.N. Spadaro's work have given a simpler alternative approach. We extend the H\older regularity for Dirichlet minimizing Q-valued functions up to the boundary assuming enough regularity of the domain and H\older regularity of the boundary data with exponent >1/2.