Kernel estimates for parabolic systems of partial differential equations with unbounded coefficients

TL;DR

This paper derives pointwise upper bounds for transition kernels of semigroups linked to nondegenerate elliptic PDE systems with unbounded, variable coefficients, advancing understanding of their behavior.

Contribution

It introduces new kernel estimates for elliptic PDE systems with unbounded, variable coefficients, extending existing theoretical frameworks.

Findings

Established pointwise upper bounds for transition kernels.

Handled systems with unbounded and variable coefficients.

Provided tools for analyzing PDE systems with complex coefficients.

Abstract

We provide pointwise upper bounds for the transition kernels of semigroups associated with a class of systems of nondegenerate elliptic partial differential equations with unbounded coefficients with possibly unbounded diffusion coefficients, which may vary equation by equation.