Abstract
The first maximum property of Cauchy's problem for a class of linear hyperbolic equations of second order was formulated by WEINBERG~R [11] for the case of two independent variables. Further results for Cauchy's problem, in the case of two independent variables, have been obtained by PROTTER [6] and GLOISTEHN [5]. In the case of more than two independent variables, WEINSTE~ [13; 14] was the first to obtain a maximum property of an initial value problem for a class of linear partial differential equations of second order that contains the wave equation. WEINSTEIN'S formulation of a maximum property of Cauchy's problem for the wave equation has been extended by CARROLL [1] to equations that admit distribution valued solutions and by WEINBERGER [12] and the author [8; 9; 10] to hyperbolic operators with variable coefficients. The main purpose of this paper is to establish the following maximum property of Cauchy's problem for the wave operator L,
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