Regularity theory for elliptic and parabolic equations in nondivergence form

Abstract

We investigate optimal regularity theory for nondivergence elliptic and parabolic equations with discontinuous coefficients in bounded domains. Global Hessian estimates of the solutions to the Dirichlet problems for such equations are obtained under the small bounded mean oscillation (BMO) condition of the coefficients in the setting of various function spaces such as weighted Lebesgue spaces, variable exponent Lebesgue spaces, weighted Orlicz spaces and weighted variable exponent Lebesgue spaces.