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Symmetry via the moving plane method for a class of quasilinear elliptic problems involving the Hardy potential

Part of: Partial differential equations

Published online by Cambridge University Press:  09 December 2022

Giusy Chirillo ,
Luigi Montoro ,
Luigi Muglia  and
Berardino Sciunzi
Giusy Chirillo
Affiliation:
Dipartimento di Matematica e Informatica, Università della Calabria, Via P. Bucci, 87036 Arcavacata di Rende (CS), Italy chirillo@mat.unical.it, montoro@mat.unical.it, muglia@mat.unical.it, sciunzi@mat.unical.it
Luigi Montoro
Affiliation:
Dipartimento di Matematica e Informatica, Università della Calabria, Via P. Bucci, 87036 Arcavacata di Rende (CS), Italy chirillo@mat.unical.it, montoro@mat.unical.it, muglia@mat.unical.it, sciunzi@mat.unical.it
Luigi Muglia
Affiliation:
Dipartimento di Matematica e Informatica, Università della Calabria, Via P. Bucci, 87036 Arcavacata di Rende (CS), Italy chirillo@mat.unical.it, montoro@mat.unical.it, muglia@mat.unical.it, sciunzi@mat.unical.it
Berardino Sciunzi
Affiliation:
Dipartimento di Matematica e Informatica, Università della Calabria, Via P. Bucci, 87036 Arcavacata di Rende (CS), Italy chirillo@mat.unical.it, montoro@mat.unical.it, muglia@mat.unical.it, sciunzi@mat.unical.it
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Abstract

We consider positive solutions to a class of quasilinear elliptic problems involving the Hardy potential under zero Dirichlet boundary condition. Via moving plane method, proving a weak comparison principle, we prove symmetry and monotonicity properties for the solutions defined on strictly convex symmetric domains.

Keywords

Quasilinear elliptic equationsHardy potentialSupercritical problemsSimmetry and Monotonicity

MSC classification

Primary: 35B06: Symmetries, invariants, etc.
Secondary: 35B09: Positive solutions 35B51: Comparison principles
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 153 , Issue 6 , December 2023 , pp. 1858 - 1882
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Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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