The skew derivative problem for the Helmholtz equation outside cuts in a plane

Abstract

The skew derivative problem for the propagative Helmholtz equation outside cuts in a plane is studied by potential theory and the boundary integral equation method. The problem is reduced to the Cauchy singular integral equation and then to the Fredholm integral equation of the second kind, which is uniquely solvable. Applications to the diffraction of long ocean waves are discussed.

Keywords

• wave scattering
• boundary value problem
• integral equations
• potential theory