A uniquely solvable integral equation for the neumann problem in linearelasticity

Abstract

Integral equation methods are often used to treat exterior problems in acoustics, electromagnetics and linear elasticity. The simplest equations are these of the second kind which are susceptible to Fredholm type theory and fail to be uniquely solvable at the so-called irregular frequencies. Inorder to avoid the nonuniqueness problem arising in this kind of equations a modified boundary integral equation for the Neumann problem in linear elasticity in R³ is proposed. The displacement field is expressed as a linear combination of a single and a double layer potentials. The unique solvability of the boundary integral equation is demonstrated by considering commutativity properties which the involved to the problem integral operators satisfy.

Keywords:

• Linear Integral Equations

AMS:

• 45A05