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September  2019, 18(5): 2819-2833. doi: 10.3934/cpaa.2019126

## 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  October 2018 Revised  January 2019 Published  April 2019

Fund Project: 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".

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.

Citation: Stefano Biagi, Enrico Valdinoci, Eugenio Vecchi. A symmetry result for elliptic systems in punctured domains. Communications on Pure & Applied Analysis, 2019, 18 (5) : 2819-2833. doi: 10.3934/cpaa.2019126
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