English

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

Analysis of PDEs 2017-12-14 v2

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.

Keywords

Cite

@article{arxiv.1709.10123,
  title  = {Dynamical boundary conditions in a non-cylindrical domain for the Laplace equation},
  author = {Pedro T. P. Lopes and Marcone C. Pereira},
  journal= {arXiv preprint arXiv:1709.10123},
  year   = {2017}
}

Comments

This is a new version of a previous paper submitted here in Arxiv. It has substantial changes from the previous one. A whole section was rewritten and some small mistakes were corrected