ON THE INTEGRABILITY OF FINITE ENERGY SOLUTIONS FOR P-HARMONIC EQUATIONS

We prove a higher integrability result for the gradient of solutions to some degenerate elliptic PDEs, whose model arises in the study of mappings with finite distortion.The nonnegative function K(x) which measures the degree of degeneracy of ellipticity bounds lies in the exponential class, i.e. exp(lambdaK(x)) is integrable for some lambda > 0.Our result states that if A is sufficiently large, then the gradient of a : finite energy" solution actually belongs to the Zygmund space L-P log(alpha) L, alpha greater than or equal to 1.