Oblique derivative problem for non-divergence parabolic equations with discontinuous in time coefficients in a wedge

TL;DR

This paper addresses oblique derivative problems for non-divergence parabolic equations with discontinuous time coefficients in a wedge, providing weighted coercive estimates in anisotropic Sobolev spaces.

Contribution

It introduces new weighted coercive estimates for solutions of non-divergence parabolic equations with discontinuous coefficients in a wedge setting.

Findings

Established weighted coercive estimates in anisotropic Sobolev spaces.

Extended analysis to equations with discontinuous in time coefficients.

Provided a framework for handling oblique derivative problems in wedge domains.

Abstract

We consider an oblique derivative problem in a wedge for nondivergence parabolic equations with discontinuous in $t$ coefficients. We obtain weighted coercive estimates of solutions in anisotropic Sobolev spaces.