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Let M and L be elliptic differential operators of orders 2m and 2/, respectively, with m ^ S. The existence and uniqueness of a solution to the abstract mixed initial and boundary value problem was established for u 0 given in the domain of the infinitesimal generator of a strongly-continuous semi-group. The purpose of this paper is to show that this semi-group is holomorphic and then obtain differentiability results for the solution and convergence of this solution to the initial function u 0doi:10.2140/pjm.1970.34.781 fatcat:oklqtv44uzavnkyz5rt25tvfi4