Monotonicity and one-dimensional symmetry of solutions for the weighted fractional parabolic equations on the whole space-Reference-Cited by-同舟云学术

Monotonicity and one-dimensional symmetry of solutions for the weighted fractional parabolic equations on the whole space

Published:2024-02-20 Issue:05 Volume:35 Page:
ISSN:0129-167X
Container-title:International Journal of Mathematics
language:en
Short-container-title:Int. J. Math.

Author:

Li Ye¹^ORCID,Lin Chuang²^ORCID,Zhang Kelei³^ORCID

Affiliation:

1. Department of Mathematical Sciences, William Rainey Harper College, Palatine, IL 60067, USA

2. School of Mathematics and Statistics, Shaanxi Normal University, Xi’an 710119, P. R. China

3. Center for Applied Mathematics of Guangxi (GUET), School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, P. R. China

Abstract

In this paper, we investigate the monotonicity and one-dimensional symmetry of solutions for parabolic equations related to the weighted fractional Laplacian on the whole space. We first establish a generalized weighted average inequality and the maximum principle in unbounded domains, and then carry out the sliding method to obtain monotonicity and one-dimensional symmetry of solutions.

Funder

Youth Innovation Team of Shaanxi Universities, Shaanxi Fundamental Science Research Project for Mathematics and Physics

Fundamental Research Funds for the Central Universities

National Natural Science Foundation of China

Publisher

World Scientific Pub Co Pte Ltd

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129167X24500101

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