Some geometric aspects of hyperbolic boundary value problems

Conrey, J. Brian; Smiley, Michael W.

doi:10.1090/S0002-9939-1989-0975635-3

Some geometric aspects of hyperbolic boundary value problems
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by J. Brian Conrey and Michael W. Smiley PDF

Proc. Amer. Math. Soc. 107 (1989), 591-601 Request permission

Abstract:

Let $L$ denote the linear operator associated with the wave equation when it is subjected to boundary conditions in both space and time. The properties of invertibility or partial invertibility of $L$, and compactness of the (partial) inverse when it exists, are characterized in terms of the space time domain $\Omega \times (0,T)$, for all rectangular domains $\Omega \subset {{\mathbf {R}}^n}$.

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