GRADIENT ESTIMATES FOR THE STRONG p(x)-LAPLACE EQUATION

We study nonlinear elliptic equations of strong p (x)-Laplacian type to obtain an interior Calderon-Zygmund type estimates by finding a correct regularity assumption on the variable exponent p (x). Our proof is based on the maximal function technique and the appropriate localization method.NSFC [11671111, 11601103, 11571020]; Natural Science Foundation of Heilongjiang Province [QC2014C002]; Heilongjiang Province Postdoctoral Special Science Foundation [LBHTZ0514]SCI(E)ARTICLE74109-41293