On the first boundary problem for a hyperbolic equation in an arbitrary cylinder

A. F. Filippov

M. V. Lomonosov Moscow State University

Abstract: A study is made of the solutions of a second-order hyperbolic equation which vanish on the boundary of an arbitrary domain in the space of the variables $x_1,\dots,x_n$ The degree of smoothness in the initial conditions, necessary and sufficient to guarantee the same degree of smoothness in the solution (considered as a function of $x_1,\dots,x_n$ for all $t$, is ascertained.

UDC: 517.9

Received: 15.02.1968

 English version: Mathematical Notes, 1968, 4:2, 601–605

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