Parabolic oblique derivative problem with discontinuous coefficients in generalized weighted Morrey spaces

Abstract

We obtain the global weighted Morrey-type regularity of the solution of the regular oblique derivative problem for linear uniformly parabolic operators with VMO coefficients. We show that if the right-hand side of the parabolic equation belongs to certain generalized weighted Morrey space M-p,M-phi (Q, omega) than the strong solution belongs to the generalized weighted Sobolev-Morrey space (W) over dot(2,1)(p,phi) (Q, omega).