Heat Kernel estimates for some elliptic operators with unbounded diffusion coefficients

TL;DR

This paper establishes heat kernel bounds for a class of elliptic operators with unbounded diffusion coefficients in Euclidean space, using advanced inequalities.

Contribution

It introduces new heat kernel estimates for operators with unbounded coefficients, expanding understanding of their behavior.

Findings

Derived heat kernel bounds for (1 + |x|^{eta})Δ operators.

Utilized Nash and weighted Hardy inequalities in proofs.

Extended classical results to unbounded coefficient cases.

Abstract

We prove heat kernel bounds for the operator (1 + |x|^{\alpha})\Delta in R^N, through Nash inequalities and weighted Hardy inequalities.