Regularity of minimizers under limit growth conditions

Abstract

It is well known that an integral of the Calculus of Variations satisfying anisotropic growth conditions may have unbounded minimizers if the growth exponents are too far apart. Under sharp assumptions on the exponents we prove the local boundedness of minimizers of functionals with anisotropic p,q-growth, via the De Giorgi method. As a by-product, regularity of minimizers of some non coercive functionals is obtained by reduction to coercive ones.