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Coercive combined field integral equations

Many boundary integral equations for exterior Dirichlet and Neumann boundary value problems for the Helmholtz equation suffer from a motorious instability for wave numbers related to interior resonances. The so-called combined field integral equations are not affected. This article presents combined field integral equations on two-dimensional closed surfaces that possess coercivity in canonical trace spaces. For the exterior Dirichlet problem the main idea is to use suitable regularizing operators in the framework of an indirect method. This permits us to apply the classical convergence theory of conforming Galerkin methods.