NONDIVERGENCE PARABOLIC EQUATIONS IN WEIGHTED VARIABLE EXPONENT SPACES

Abstract

We prove the global Calderon-Zygmund estimates for second order parabolic equations in nondivergence form in weighted variable exponent Lebesgue spaces. We assume that the associated variable exponent is log-Holder continuous, the weight is of a certain Muckenhoupt class with respect to the variable exponent, the coefficients of the equation are the functions of small bonded mean oscillation, and the underlying domain is a C-1,C-1-domain.