A symmetry result for elliptic systems in punctured domains

Stefano Biagi, Enrico Valdinoci, Eugenio Vecchi

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)2819-2833
Number of pages15
JournalCommunications on Pure and Applied Analysis
Volume18
Issue number5
DOIs
Publication statusPublished - 1 Sep 2019

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Elliptic Systems
Symmetry
Boundary conditions
Hyperplane
System of equations
Bounded Domain
Monotone

Cite this

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A symmetry result for elliptic systems in punctured domains. / Biagi, Stefano; Valdinoci, Enrico; Vecchi, Eugenio.

In: Communications on Pure and Applied Analysis, Vol. 18, No. 5, 01.09.2019, p. 2819-2833.

Research output: Contribution to journalArticle

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AU - Valdinoci, Enrico

AU - Vecchi, Eugenio

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N2 - 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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