Weconsideranellipticsystemofequationsinapuncturedbounded 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 symme- try results also for a related polyharmonic problem of any order with Navier boundary conditions.

A symmetry result for elliptic systems in punctured domains

Stefano Biagi;VECCHI, EUGENIO
2019

Abstract

Weconsideranellipticsystemofequationsinapuncturedbounded 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 symme- try results also for a related polyharmonic problem of any order with Navier boundary conditions.
Elliptic systems, moving plane method, symmetry of solutions.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11311/1125164
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