H^2-regularity for a two-dimensional transmission problem with geometric constraint

TL;DR

This paper proves H^2-regularity for solutions to a 2D transmission problem with geometric constraints, even when the domain includes non-Lipschitz cusp points, and shows solutions depend continuously on domain changes.

Contribution

It establishes H^2-regularity for a 2D transmission problem with complex geometric features, extending regularity results to non-Lipschitz domains with cusps.

Findings

H^2-regularity holds despite cusp points.

Solutions depend continuously on domain variations.

Non-Lipschitz domains do not cause regularity breakdown.

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.