A nonlinear interpolation result with application to the summability of minima of some integral functionals

Abstract

We shall prove results asserting the (global)$L^s$-summability of the minima of integralfunctionals, using the classical structural assumptions. A featureof the method is that it depends not so much on the minimization problem but rather on the'control from below'' of the structural assumptions. Then the proof concerning thesummability of the minima of integral functionals can be easily adapted in order to prove thesummability of solutions of nonlinear elliptic equations (even when they are not Euler equations offunctionals).