Boundary behavior of positive solutions of the heat equation on a stratified Lie group

Article Type

Research Article

Publication Title

Bulletin des Sciences Mathematiques

Abstract

In this article, we are concerned with a certain type of boundary behavior of positive solutions of the heat equation on a stratified Lie group at a given boundary point. We prove that a necessary and sufficient condition for the existence of the parabolic limit of a positive solution u at a point on the boundary is the existence of the strong derivative of the boundary measure of u at that point. Moreover, the parabolic limit and the strong derivative are equal. We also construct an example of a positive measure on the Heisenberg group to show that the set of all points where strong derivative exists is strictly larger than the set of Lebesgue points of the measure.

DOI

https://10.1016/j.bulsci.2023.103324

Publication Date

11-1-2023

Comments

Open Access, Green

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