Regularity of minimizing sequences for functionals of the calculus of variations via the Ekeland principle

Abstract

(Ω), and Ω is an open, bounded subset of RN, N≥ 2. Various regularity results are known for the minima of J, depending on the regularity of the integrand f with respect to x, u and∇ u. We are going to show that if a minimum u of J has a certain regularity (say, u belongs to L1 ...