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.
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© 2008 Springer Science+Business Media, LLC
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(2008). Variational Methods. In: Numerical Approximation Methods for Elliptic Boundary Value Problems. Springer, New York, NY. https://doi.org/10.1007/978-0-387-68805-3_3
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DOI: https://doi.org/10.1007/978-0-387-68805-3_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-31312-2
Online ISBN: 978-0-387-68805-3
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