Elliptic and Parabolic Equations - Abstract

Softova, Lubomira G.

Boundary value problems in generalized Morrey spaces

We study strong solvability for two kind of boundary problems for linear uniformly parabolic operators with VMO coefficients. The right-hand side belongs to the generalized Morrey spaces with weight satisfying suitable bubbling and integral conditions. It is obtained continuity of singular and non singular integrals that permits to prove a priori estimates and unique solvability of the Dirichlet and oblique derivative problem in generalized Sobolev--Morrey spaces.