The functional calculus approach

Tobias Nau

Chapter 10 in Lp-Theory of Cylindrical Boundary Value Problems, 2012, pp 153-169 from Springer

Abstract: Abstract 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].

Keywords: Banach Space; Dirichlet Boundary Condition; Lipschitz Domain; Canonical Extension; Bound Lipschitz Domain (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-3-8348-2505-6_10

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