Symmetry and monotonicity property of a solution of Laplacian equation with singular terms
Ritabrata Jana
Indian Institute of Science Education and Research, Trivandrum (IISER-TVM), Thiruvananthapuram, India
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Abstract
This paper examines the behavior of a positive solution of the Laplace equation with a singular term and zero Dirichlet boundary condition. Specifically, we consider the equation
We assume that , , and is a nondecreasing function. Our analysis uses the moving plane method to investigate the symmetry and monotonicity properties of . Additionally, we establish a strong comparison principle for solutions of the Laplace equation with radial symmetry under the assumptions that and .
Cite this article
Ritabrata Jana, Symmetry and monotonicity property of a solution of Laplacian equation with singular terms. Z. Anal. Anwend. 42 (2023), no. 3/4, pp. 483–502
DOI 10.4171/ZAA/1746