Parabolic oblique derivative problem in generalized Morrey spaces

TL;DR

This paper investigates the regularity of solutions to parabolic equations with oblique derivatives, demonstrating that solutions belong to specific Sobolev-Morrey spaces when the right-hand side is in a generalized Morrey space.

Contribution

It establishes new regularity results for parabolic equations with VMO coefficients in generalized Morrey spaces, linking the right-hand side's space to solution regularity.

Findings

Solutions belong to Sobolev-Morrey spaces under certain conditions.

Regularity results depend on the right-hand side's membership in generalized Morrey spaces.

The study extends regularity theory for parabolic equations with VMO coefficients.

Abstract

We study the regularity of the solutions of the oblique derivative problem for linear uniformly parabolic equations with VMO coefficients. We show that if the right-hand side of the parabolic equation belongs to certain generalized Morrey space than the strong solution belongs to the corresponding generalized Sobolev-Morrey space.