Abstract
AbstractIn this paper we present new methods to solve the classical Dirichlet and Neumann problems for ΔU + k2U = 0. We prove that the solutions of this equation for a region S containing G restricted to G are dense in L2(∂G). Introducing a basis in the space of solutions for S we find a complete orthogonal system in L2(∂G) which can be used to solve the boundary value problems by means of approximation in the Hilbertspace norm. Regularity estimates lead to series expansions in G.The well‐known basis systems obtained by separation of variables thus may be used for every regular region without the very special geometric restrictions. Another class of basis systems may be obtained in analogy to the Runge. theorems by considering types of singularity functions.
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