Symmetry and Monotonicity of Solutions to Mixed Local and Nonlocal Weighted Elliptic Equations

Abstract

This paper focuses on the symmetry and monotonicity of non-negative solutions to a mixed local and nonlocal weighted elliptic problem. This problem generalizes the ground-state representation of elliptic equations with the Hardy potential. The novelty of this research lies in developing the moving planes method for mixed local and nonlocal equations with a weighted function, thus clarifying the influence of the weighted function on the solution properties.

Keywords

• mixed local and nonlocal
• symmetry
• monotonicity
• moving planes method