THE LIMITING ABSORPTION PRINCIPLE FOR THE TWO-DIMENSIONAL INHOMOGENEOUS ANISOTROPIC ELASTICITY SYSTEM
Resource
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 358 (1): 147-165
Journal
Transactions of the American Mathematical Society
Journal Volume
358
Journal Issue
1
Pages
147-165
Date Issued
2006
Date
2006
Author(s)
NAKAMURA, GEN
Abstract
In this work we establish the limiting absorption principle for the two-dimensional steady-state elasticity system in an inhomogeneous anisotropic medium. We then use the limiting absorption principle to prove the existence of a radiation solution to the exterior Dirichlet or Neumann boundary value problems for such a system. In order to define the radiation solution, we need to impose certain appropriate radiation conditions at infinity. It should be remarked that even though in this paper we assume that the medium is homogeneous outside of a large domain, it still preserves anisotropy. Thus the classical Kupradze's radiation conditions for the Isotropie system are not suitable in our problem and new radiation conditions are required. The uniqueness of the radiation solution plays a key role in establishing the limiting absorption principle. To prove the uniqueness of the radiation solution, we make use of the unique continuation property, which was recently obtained by the authors. The study of this work is motivated by related inverse problems in the anisotropic elasticity system. The existence and uniqueness of the radiation solution are fundamental questions in the investigation of inverse problems. © 2004 American Mathematical Society.
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journal article
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