Local Boundedness for Minimizers of Some Polyconvex Integrals

We prove a regularity result for local minimizers of a vector-valued special class of polyconvex functionals. Under some structure assumptions on the energy density, we prove that local minimizers u are locally bounded. First, for each component , we prove a Caccioppoli’s inequality and then apply De Giorgi’s iteration method to get the boundedness of minimizer.