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Full low-frequency asymptotic expansion for second-order elliptic equations in two dimensions

✍ Scribed by R. Kleinman; B. Vainberg

Publisher
John Wiley and Sons
Year
1994
Tongue
English
Weight
739 KB
Volume
17
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

The present paper contains the low‐frequency expansions of solutions of a large class of exterior boundary value problems involving second‐order elliptic equations in two dimensions. The differential equations must coincide with the Helmholtz equation in a neighbourhood of infinity, however, they may depart radically from the Helmholtz equation in any bounded region provided they retain ellipticity. In some cases the asymptotic expansion has the form of a power series with respect to k^2^ and k^2^ (ln k + a)^−1^, where k is the wave number and a is a constant. In other cases it has the form of a power series with respect to k^2^, coefficients of which depend polynomially on In k. The procedure for determining the full low‐frequency expansion of solutions of the exterior Dirichlet and Neumann problems for the Helmholtz equation is included as a special case of the results presented here.

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