On parabolic convergence of positive solutions of the heat equation

Authors

Jayanta Sarkar, Indian Statistical Institute, Kolkata

Article Type

Research Article

Publication Title

Complex Variables and Elliptic Equations

Abstract

In this article, we study a certain type of boundary behaviour of positive solutions of the heat equation on the Euclidean upper half-space of (Formula presented.). We prove that the existence of the parabolic limit of a positive solution of the heat equation at a point in the boundary is equivalent to the existence of the strong derivative of the boundary measure of the solution at that point. Moreover, the parabolic limit and the strong derivative are equal.

First Page

1409

Last Page

1425

DOI

10.1080/17476933.2021.1882432

Publication Date

1-1-2022

Comments

Open Access, Green

Recommended Citation

Sarkar, Jayanta, "On parabolic convergence of positive solutions of the heat equation" (2022). Journal Articles. 3425.
https://digitalcommons.isical.ac.in/journal-articles/3425