Symmetry results for the solutions of a partial differential equation arising in water waves

2019/01/11 by Dipierro, Serena, Miraglio, Pietro, Valdinoci, Enrico
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1901.03581

Abstract

This paper recalls some classical motivations in fluid dynamics leading to a partial differential equation which is prescribed on a domain whose boundary possesses two connected components, one endowed with a Dirichlet datum, and the other endowed with a Neumann datum. The problem can also be reformulated as a nonlocal problem on the component endowed with the Dirichlet datum. A series of recent symmetry results are presented and compared with the existing literature.

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