The Dirichlet Problem for Non-divergence Parabolic Equations with Discontinuous in Time Coefficients

TL;DR

This paper derives pointwise Green function estimates for non-divergence parabolic equations with discontinuous time coefficients, enabling solvability results in weighted Lebesgue spaces.

Contribution

It introduces new pointwise Green function estimates for parabolic equations with discontinuous in time coefficients, leading to solvability in anisotropic weighted spaces.

Findings

Established pointwise Green function estimates.

Proved coercive estimates in weighted Lebesgue spaces.

Demonstrated solvability theorems for the Dirichlet problem.

Abstract

We establish pointwise estimates for the Green function to the Dirichlet problem for parabolic equation with coefficients measurable in time variable. Using these estimate we obtain coercive estimates for this problem in anisotropic weighted Lebesgue spaces and prove the solvability theorems.