Morrey-Campanato estimates for Helmholtz equations with two unbounded media

Elise Fouassier (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We prove uniform Morrey-Campanato estimates for Helmholtz equations in the case of two unbounded inhomogeneous media separated by an interface. They imply weighted $L^2$-estimates for the solution. We prove also a uniform $L^2$-estimate {\em without weight} for the trace of the solution on the interface

Mots clés: two unbounded media; Helmholtz equations

Domaines: Equations aux dérivées partielles [math.AP]

Elise Fouassier. Morrey-Campanato estimates for Helmholtz equations with two unbounded media. Proceedings of the Royal Society of Edinburgh: Section A, Mathematics, 2005, 135 (4), pp.767-776. ⟨hal-00004257⟩