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arXiv · 1709.10123

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

Pedro T. P. Lopes·Marcone C. Pereira
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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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Pedro T. P. Lopes, Marcone C. Pereira. 2017-12-13. Dynamical boundary conditions in a non-cylindrical domain for the Laplace equation. https://arxiv.org/abs/1709.10123

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