The Question of Solvability
In this chapter we prove the existence of regular solutions to the interior and exterior Dirichlet and Neumann boundary value problems introduced in Section 4.2. This is done by means of an indirect boundary integral equation method in which the solution of each problem is sought in the form of a particular potential. Such a method has been used successfully to prove the solvability of a variety of important boundary value problems, for example, in connection with the Helmholtz equation (see ) and stationary oscillations in classical three-dimensional elasticity (see ). The above models have many characteristics in common with our system of equations, an important one being the presence of eigenfrequencies.
KeywordsRegular Solution Boundary Integral Equation Helmholtz Equation Zero Solution Stationary Oscillation
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