The functional calculus approach
This chapter extends the results from Chapter 8 in two directions. Firstly, domains given as the Cartesian product of finitely many standard domains are considered. Secondly, with a Banach space F, the cylindrical boundary value problems are F-valued and contain L(F)-valued coefficients. Here we employ the operator-valued Dunford calculus and the Kalton-Weis-Theorem. Again we first consider rather arbitrary cylindrical boundary value problems and focus on the Laplacian at the end. The results of this chapter also appear in [NS11a].
KeywordsBanach Space Dirichlet Boundary Condition Lipschitz Domain Canonical Extension Bound Lipschitz Domain
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