We also collect in this chapter the relevant mapping properties and jump relations for the boundary potentials (or Poisson operators) as well as for the volume potentials, which are covered by Boutet de Monvel's work for even more general pseudodifferential operators satisfying the transmission conditions including those of operators with symbols of rational type.
The last section is devoted to the concept of strong ellipticity and Fredholm properties of boundary pseudodifferential operators.
The presentation of this chapter is partially based on the book by Chazarain and Piriou [39], the PHD dissertation by Kieser [156] and Hörmander's book [131, Vol. III] and covers only a small part of Boutet de Monvel's analysis (see [19, 20, 21], Grubb [110] and Schulze [273]).
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© 2008 Springer-Verlag Berlin Heidelberg
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(2008). Pseudodifferential and Boundary Integral Operators. In: Boundary Integral Equations. Applied Mathematical Sciences, vol 164. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68545-6_8
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DOI: https://doi.org/10.1007/978-3-540-68545-6_8
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