  In this paper, we present results about the existence and uniqueness of
solutions of elliptic equations with transmission and Wentzell boundary
conditions. We provide Schauder estimates and existence results in H\"older
spaces. As an application, we develop an existence theory for small-amplitude
two-dimensional traveling waves in an air-water system with surface tension.
The water region is assumed to be irrotational and of finite depth, and we
permit a general distribution of vorticity in the atmosphere.
