Dynamical boundary conditions in a non-cylindrical domain for the Laplace equation

2017/09/28 by Lopes, Pedro T. P., Pereira, Marcone C.
#35B40 #35K10 #47A07 #47D06 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1709.10123

Abstract

In this paper, we study existence, uniqueness and asymptotic behavior of the Laplace equation with dynamical boundary conditions on regular non-cylindrical domains. We write the problem as a non-autonomous Dirichlet-to-Neumann operator and use form methods in a more general framework to accomplish our goal. A class of non-autonomous elliptic problems with dynamical boundary conditions on Lipschitz domains is also considered in this same context.

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