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 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; Enrico Valdinoci; VECCHI, EUGENIO. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - STAMPA. - 18:5(2019), pp. 2819-2833. [10.3934/cpaa.2019126]
A symmetry result for elliptic systems in punctured domains
VECCHI, EUGENIO
2019
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 symme- try results also for a related polyharmonic problem of any order with Navier boundary conditions.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.