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On Density and Approximation Properties of Special Solutions of the Helmohltz Equation
Author(s) -
Still G.
Publication year - 1992
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19920720711
Subject(s) - mathematics , helmholtz equation , eigenvalues and eigenvectors , infimum and supremum , separation of variables , mathematical analysis , operator (biology) , laplace transform , laplace's equation , helmholtz free energy , norm (philosophy) , partial differential equation , physics , boundary value problem , biochemistry , chemistry , repressor , quantum mechanics , transcription factor , gene , political science , law
Abstract We consider eigenvalue problems for the Laplace operator on a region G. Especially if G is simply‐shaped, defect‐minimization methods with trial functions φ satisfying the Helmholtz equation Δφ + λφ = 0 may be suitable for the numerical solution of the problem. Such functions φ are given for example by the classical method of separation of variables. This paper is concerned with density and approximation properties of these special solutions of the Helmholtz equation with respect to the supremum‐norm.