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We use the theory of boundary values (also called traces) of holomorphic semigroups as developed by Boyadzhiev-deLaubenfels (1993) and El-Mennaoui (1992) to study the second order Cauchy problem for certain generators of holomorphic semigroups. Our results contain in particular the result of Hieber (Math. Ann. 291 (1991), 1–16) for the Laplace operator on Lp(RN ).

Trace theorems for holomorphic semigroups and the second order Cauchy problem