The weak formulation of boundary value problems leads to variational problems and associated operator equations. In particular, the representation of solutions of partial differential equations by using surface and volume potentials requires the solution of boundary integral operator equations to find the complete Cauchy data. In this chapter we describe the basic tools from functional analysis which are needed to investigate the unique solvability of operator equations.


Unique Solution Variational Method Variational Problem Operator Equation Bounded Linear Operator 
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© Springer Science+Business Media, LLC 2008

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