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Research Article | Open Access

Qualitative properties of solutions to the Dirichlet problem for a Laplace equation involving the Hardy potential with possibly boundary singularity

Luigi Montoro( ), Berardino Sciunzi
Dipartimento di Matematica e Informatica, UNICAL, Ponte Pietro Bucci 31B, 87036 Arcavacata di Rende, Cosenza, Italy
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Abstract

We consider positive solutions to semilinear elliptic problems with Hardy potential and a first order term in bounded smooth domain Ω with 0 ∈ Ω ¯ . We deduce symmetry and monotonicity properties of the solutions via the moving plane procedure under suitable assumptions on the nonlinearity.

Keywords

semilinear elliptic equationsHardy potentialqualitative properties

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Mathematics in Engineering
Volume 5 Issue 1,
February 2023
Pages 1-16
DOI: 10.3934/mine.2023017

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Cite this article:
Montoro L, Sciunzi B. Qualitative properties of solutions to the Dirichlet problem for a Laplace equation involving the Hardy potential with possibly boundary singularity. Mathematics in Engineering, 2023, 5(1): 1-16. https://doi.org/10.3934/mine.2023017

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Received: 16 November 2021
Revised: 01 February 2022
Accepted: 09 February 2022
Published: 15 February 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)