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Well-posedness of hyperbolic initial boundary value problems. (English) Zbl 1078.35066
Summary: Assuming that a hyperbolic initial boundary value problem satisfies an a priori energy estimate with a loss of one tangential derivative, we show a well-posedness result in the sense of Hadamard. The coefficients are assumed to have only finite smoothness in view of applications to nonlinear problems. This shows that the weak Lopatinskii condition is roughly sufficient to ensure well-posedness in appropriate functional spaces.

MSC:
35L50 Initial-boundary value problems for first-order hyperbolic systems
35L40 First-order hyperbolic systems
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