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 Mp,ϕ(Q, w), than the strong solution belongs to the generalized weighted Sobolev- Morrey space W˙2,1p,φ(Q,ω)$\dot W_{2,1}^{p,\varphi }\left( {Q,\omega } \right)$.

Keywords

• generalized weighted morrey spaces
• uniformly parabolic operators
• regular oblique derivative problem
• vmo
• 35k20
• 35d35
• 35b45
• 35r05