On Morrey and BMO regularity for gradients of minima of certain non-differentiable functionals

Abstract

We consider minima of variational integrals with non-differentiable integrands in the form f (x, u, Du) = < A(x)Du, Du > + g(x, u, Du). Assuming that the part g(x, u, z) is equipped by sub-quadratic growth in z only for big value of vertical bar z vertical bar (but the growth is arbitrarily close to the quadratic one), we prove the everywhere Morrey and BMO regularity for gradients of minima.