Generalized Morrey regularity for parabolic equations with discontinuity data

TL;DR

This paper establishes generalized Morrey space regularity for solutions of linear parabolic equations with discontinuous coefficients, using Calderón-Zygmund operators and VMO functions, leading to insights on global solution regularity.

Contribution

It introduces new regularity results in generalized Morrey spaces for parabolic equations with discontinuous data, extending existing theories.

Findings

Continuity of sublinear integrals in generalized parabolic Morrey spaces.

Regularity estimates for solutions of parabolic equations with discontinuous coefficients.

Application of Calderón-Zygmund operators and VMO functions to parabolic regularity.

Abstract

We obtain continuity in generalized parabolic Morrey spaces of sublinear integrals generated by the parabolic Calder\'{o}n-Zygmund operators and its commutator with $VMO$ functions. The obtained estimates are used to study global regularity of the solutions of the Cauchy-Dirichlet problem for linear uniformly parabolic equations with discontinuous coefficients.