Iterated Neumann problem for the higher order Poisson equation

Abstract:

Rewriting the higher order Poisson equation Δnu = f in a plane domain as a system of Poisson equations it is immediately clear what boundary conditions may be prescribed in order to get (unique) solutions. Neumann conditions for the Poisson equation lead to higher-order Neumann (Neumann-n) problems for Δnu = f. Extending the concept of Neumann functions for the Laplacian to Neumann functions for powers of the Laplacian leads to an explicit representation of the solution to the Neumann-n problem for Δnu = f. The representation formula provides the tool to treat more general partial differential equations with leading term Δnu in reducing them into some singular integral equations. © 2006 WILEY-VCH Verlag GmbH & Co. KGaA.

Año de publicación:

2006

Keywords:

• Neumann problem
• Poisson equation
• integral representations
• Higher order Neumann functions

Fuente:

scopus