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

Luigi Montoro; Berardino Sciunzi; Luigi Montoro; Berardino Sciunzi

doi:10.3934/mine.2023017

Mathematics in Engineering

2023, Volume 5, Issue 1: 1-16. doi: 10.3934/mine.2023017

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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

Received: 16 November 2021 Revised: 01 February 2022 Accepted: 09 February 2022 Published: 01 March 2022

We consider positive solutions to semilinear elliptic problems with Hardy potential and a first order term in bounded smooth domain $ \Omega $ with $ 0\in \overline \Omega $. We deduce symmetry and monotonicity properties of the solutions via the moving plane procedure under suitable assumptions on the nonlinearity.
- semilinear elliptic equations,
- Hardy potential,
- qualitative properties
Citation: Luigi Montoro, Berardino Sciunzi. Qualitative properties of solutions to the Dirichlet problem for a Laplace equation involving the Hardy potential with possibly boundary singularity[J]. Mathematics in Engineering, 2023, 5(1): 1-16. doi: 10.3934/mine.2023017

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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 $ \Omega $ with $ 0\in \overline \Omega $. We deduce symmetry and monotonicity properties of the solutions via the moving plane procedure under suitable assumptions on the nonlinearity.

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