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On the mixed problems for hyperbolic equations of second order, only the problems with the Dirichlet condition and with the Neumann condition are studied satisfactorily. Concerning the problems with the other boundary conditions Agmon [1] contains the results on more general boundary conditions in the case when the domain is a half space and the coefficients are constant. And the author showed the not well-posedness in L 2-sense of the problem for the wave equation with an oblique derivative boundary condition [7]. In this paper we extend the results for second order equations of Agmon's paper to the case of variable coefficients and a general domain.

A mixed problem for hyperbolic equations of second order with a first order derivative boundary condition