A symmetry result for elliptic systems in punctured domains

Stefano Biagi; Enrico Valdinoci; Eugenio Vecchi

doi:10.3934/cpaa.2019126

Article Contents

2019, Volume 18, Issue 5: 2843-2857. Doi: 10.3934/cpaa.2019126

This issue Previous Article Pointwise estimates of solutions to conservation laws with nonlocal dissipation-type terms Next Article Homoclinic orbits for a class of asymptotically quadratic Hamiltonian systems

A symmetry result for elliptic systems in punctured domains

1.
Dipartimento di Ingegneria Industriale e Scienze Matematiche, Università Politecnica della Marche, Via Brecce Bianche, 60131, Ancona, Italy
2.
Department of Mathematics and Statistics, University of Western Australia, 35 Stirling Highway, WA 6009 Crawley, Australia
3.
Dipartimento di Matematica, Università degli Studi di Trento, Via Sommarive 14, 38123, Povo (Trento), Italy

Received: September 30, 2018

Revised: December 31, 2018

Published: March 2019

The authors are members of INdAM/GNAMPA. The first and the third author are partially supported by the INdAM-GNAMPA Project 2018 "Problemi di curvatura relativi ad operatori ellittico-degeneri". The second author is supported by the Australian Research Council Discovery Project 170104880 NEW "Nonlocal Equations at Work"

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Abstract

We consider an elliptic system of equations in a punctured bounded domain. We prove that if the domain is convex in one direction and symmetric with respect to the reflections induced by the normal hyperplane to such a direction, then the solution is necessarily symmetric under this reflection and monotone in the corresponding direction. As a consequence, we prove symmetry results also for a related polyharmonic problem of any order with Navier boundary conditions.

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Mathematics Subject Classification: 35J47, 35B06, 31B30, 35J40.

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