H^2-regularity for a two-dimensional transmission problem with geometric constraint
Analysis of PDEs
2021-03-15 v1
Abstract
The H^2-regularity of variational solutions to a two-dimensional transmission problem with geometric constraint is investigated, in particular when part of the interface becomes part of the outer boundary of the domain due to the saturation of the geometric constraint. In such a situation, the domain includes some non-Lipschitz subdomains with cusp points, but it is shown that this feature does not lead to a regularity breakdown. Moreover, continuous dependence of the solutions with respect to the domain is established.
Cite
@article{arxiv.2103.07301,
title = {H^2-regularity for a two-dimensional transmission problem with geometric constraint},
author = {Philippe Laurençot and Christoph Walker},
journal= {arXiv preprint arXiv:2103.07301},
year = {2021}
}