# Accession Number:

## AD0258240

# Title:

## ASYMPTOTIC BEHAVIOR OF THE SPECTRAL MATRIX OF THE OPERATOR OF ELASTICITY

# Descriptive Note:

# Corporate Author:

## LIEGE UNIV (BELGIUM)

# Personal Author(s):

# Report Date:

## 1961-01-01

# Pagination or Media Count:

## 1.0

# Abstract:

Let D be a bounded , open , and connected domain in R3 with boundary D set Lv b2grad div v - a2 rot rot v with a , b constant. The object of this paper is to find the asymptotic representation of the spectral matrix of the problem Lv v 0 , x D , v 0 , x D , a parameter. If D is sufficiently smooth, this problem determines a sequence k of positive eigenvalues such that k when k each k is associated with an eigenfunction vk with components vkj. Set , k k , and x 3i1 iix,x . With the aid of a Tauberian theorem one arrives at the result x 6 12 a32 b31 32. Author