Spectral Problems for the Lamé System with Spectral Parameter in Boundary Conditions on Smooth or Nonsmooth Boundary

Abstract

. The paper is devoted to four spectral problems for the Lame system of linear elasticity in domains of R 3 with compact connected boundary S. The frequency is xed in the upper closed half-plane; the spectral parameter enters into the boundary or transmission conditions on S. Two cases are investigated: (1) S is C 1 ; (2) S is Lipschitz. INTRODUCTION In this paper we consider four spectral problems for the Lame system of linear elasticity, see (1.3). The system contains the frequency parameter !, which is a xed complex number with Re! > 0. The statements of Problems I{IV are given in Subsection 1.1. The spectral parameter enters into the boundary conditions (in Problems I, II) or transmission conditions (in Problems III, IV) on a closed connected surface S, which divides its complement into a bounded domain G + and an unbounded domain G . This surface is assumed to be innitely smooth in Section 1 and Lipschitz in Section 2. Our aim is to study the spectral properties ...