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
2019-01-01
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.File in questo prodotto:
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S. Biagi, E. Valdinoci, E. Vecchi - A symmetry result for elliptic systems in punctured domains.pdf
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