Mixed Biharmonic Dirichlet-Neumann Problem in Exterior Domains

Zeta Functions with Dirichlet and Neumann Boundary Conditions for Exterior Domains

We generalize earlier studies on the Laplacian for a bounded open domain 2 R 2 with connected complement and piecewise smooth boundary. We compare it with the quantum mechanical scattering operator for the exterior of this same domain. Using single layer and double layer potentials we can prove a number of new relations which hold when one chooses independently Dirichlet or Neumann boundary con...

Shift Theorems for the Biharmonic Dirichlet Problem

We consider the biharmonic Dirichlet problem on a polygonal domain. Regularity estimates in terms of Sobolev norms of fractional order are proved. The analysis is based on new interpolation results which generalizes Kellogg’s method for solving subspace interpolation problems. The Fourier transform and the construction of extension operators to Sobolev spaces on R are used in the proof of the i...

Multigrid Preconditioning for the Biharmonic Dirichlet Problem

A multigrid preconditioning scheme for solving the Ciarlet-Raviart mixed method equations for the biharmonic Dirichlet problem is presented. In particular, a Schur complement formulation for these equations which yields non-inherited quadratic forms is considered. The preconditioning scheme is compared with a standard W-cycle multigrid iteration. It is proved that a Variable V-cycle preconditio...

Multiplicity of Solutions for a Class of Quasilinear Problem in Exterior Domains with Neumann Conditions

Boundary Integral Equations for the Biharmonic Dirichlet Problem on Nonsmooth Domains

In this paper we study boundary integral formulations of the interior and exterior Dirichlet problem for the bi{Laplacian in a plane domain with a piecewise smooth boundary having corner points. The mapping properties of single and double layer bihar-monic potentials, of the Calderon projections and the Poincar e-Steklov operators for such domains are analysed. We derive direct boundary integra...