Work

The Radial Symmetry and Monotonicity of Solutions of Fractional Parabolic Equations in the Unit Ball

Year: 2025

Type: article

Abstract: We use the method of moving planes to prove the radial symmetry and monotonicity of solutions of fractional parabolic equations in the unit ball. Since the fractional Laplacian operator is a linear operator, we investigate the maximal regularity of nonlocal parabolic fractional Laplacian equations in the unit ball. The maximal regularity of nonlocal parabolic fractional Laplacian equations guarantees the existence of solutions in the unit ball. Based on these conditions, we first establish a maximum principle in a parabolic cylinder, and the principles provide a starting position to apply the method of moving planes. Then, we consider the fractional parabolic equations and derive the radial symmetry and monotonicity of solutions in the unit ball.

Source: Symmetry

DOI: 10.3390/sym17050781

Author: Xingyu Liu

Institutions: Hong Kong Polytechnic University, Yeshiva University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funders: Yeshiva University, Hong Kong Polytechnic University, Shenzhen Research Institute, City University of Hong Kong