R-sectoriality of cylindrical boundary value problems

Abstract

We prove R-sectoriality or, equivalently, Lp-maximal regularity for a class of operators on cylindrical domains of the form ℝn-k × V, where V ⸦ ℝk is a domain with compact boundary, ℝk, or a half-space. Instead of extensive localization procedures, we present an elegant approach via operatorvalued multiplier theory which takes advantage of the cylindrical shape of both, the domain and the operator.