THE HIGHER INTEGRABILITY AND THE VALIDITY OF THEEULER-LAGRANGE EQUATION FOR SOLUTIONS TOVARIATIONAL PROBLEMS

摘要

We prove higher integrability properties of solutions to the problem of minimiz-ing ∫_ΩL(x,u(x),△u(x))dx, where ζ→L(x,ζ) is a convex function satisfying some additional conditions. As an application, we prove the validity of the Euler-Lagrange equation for a class of functionals with growth faster than exponential.