On the determination of Dirichlet or transmission eigenvalues from far field data

被引：109

作者：

Cakoni, Fioralba ^{[1
]}

Colton, David ^{[1
]}

Haddar, Houssem ^{[2
,3
]}

机构：

[1] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

[2] INRIA Saclay Ile France, F-91128 Palaiseau, France

[3] Ecole Polytech CMAP, F-91128 Palaiseau, France

来源：

COMPTES RENDUS MATHEMATIQUE | 2010年 / 348卷 / 7-8期

关键词：

D O I：

10.1016/j.crma.2010.02.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the Herglotz wave function with kernel the Tikhonov regularized solution of the far field equation becomes unbounded as the regularization parameter tends to zero iff the wavenumber k belongs to a discrete set of values. When the scatterer is such that the total field vanishes on the boundary, these values correspond to the square root of Dirichlet eigenvalues for -Delta. When the scatterer is a nonabsorbing inhomogeneous medium these values correspond to so-called transmission eigenvalues. (C) 2010 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

引用

页码：379 / 383

页数：5

共 10 条

[1]

[Anonymous], 2006, QUALITATIVE METHODS

[2] Why linear sampling works [J].