On the Green's matrices of strongly parabolic systems of second order

TL;DR

This paper develops a unified method to establish existence and estimates of Green's matrices for strongly parabolic systems, applicable to both scalar and vector cases, under interior Hölder continuity assumptions.

Contribution

It introduces a general approach for constructing Green's matrices for second order strongly parabolic systems in arbitrary domains, extending previous scalar-focused results.

Findings

Existence of Green's matrices established under Hölder continuity.

Provides estimates for Green's matrices in divergence form systems.

Applicable to both scalar and vector systems.

Abstract

We establish existence and various estimates of fundamental matrices and Green's matrices for divergence form, second order strongly parabolic systems in arbitrary cylindrical domains under the assumption that solutions of the systems satisfy an interior H\"{o}lder continuity estimate. We present a unified approach valid for both the scalar and the vectorial cases.