Conformal Mapping of Regions Bounded by Curvilinear Polygons

On Conformal Mapping^of Regions Bounded by Smooth Curves

An explicit expression in terms of these parameters is obtained for AP. The fact that the integral in (3) remains bounded for 0^p<l under the assumption that C has continuously turning tangents was proved in an earlier paper of the writer [4, p. 362 j.1 The emphasis in the present note is upon the fact that the constant Ap depends only on the parameters indicated and is expressed explicitly in ...

High frequency scattering by convex curvilinear polygons

We consider scattering of a time-harmonic acoustic incident plane wave by a sound soft convex curvilinear polygon with Lipschitz boundary. For standard boundary or finite element methods, with a piecewise polynomial approximation space, the number of degrees of freedom required to achieve a prescribed level of accuracy grows at least linearly with respect to the frequency of the incident wave. ...

Numerical Conformal Mappings for Regions Bounded by Smooth Curves

v Sammanfattning vi Acknowledgments viii

On Conformal Mapping of Nearly Circular Regions

Green’s Identity in Curvilinear Polygons

For PDE examples illuminating the feedback (Redheffer product) theory of conservative boundary control systems, we need to verify conservativity of various hyperbolic PDE’s in domains Ω that have Lipschitz boundaries. A properly rigged version of Green’s Identity is then required on such domains where technical assumptions on functions at the corners of ∂Ω cannot be tolerated; such as present i...