Heat content estimates over sets of finite perimeter

TL;DR

This paper analyzes the small-time behavior of heat content in finite perimeter sets using analytic tools, with applications to rotationally invariant stable process heat kernels.

Contribution

It introduces a new approach to studying heat content over finite perimeter sets and applies it to stable process heat kernels.

Findings

Characterization of small-time heat content behavior

Application to rotationally invariant α-stable processes

Use of set covariance functions in analysis

Abstract

This paper studies by means of standard analytic tools the small time behavior of the heat content over a bounded Lebesgue measurable set of finite perimeter by working with the set covariance function and by imposing conditions on the heat kernels. Applications concerning the heat kernels of rotational invariant $\alpha$-stable processes are given.