In this paper we show that the Lp -realization of a vector-valued elliptic boundary value problem (A, Bj) admits a bounded H∞-calculus on LP(G; E), 1 <p <∞, provided the top-order coefficients of A are Hölder continuous. Here G denotes a domain in ℝn with compact C2m- boundary and E a Banach space of class HT. Our proof is based on an abstract perturbation result for operators admitting bounded H∞-calculus and kernel estimates for the solution of (A, Bj).
|Number of pages||39|
|Publication status||Published - 2004 Apr|
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