Abstract
As a graduate student back in 1953–54 I struggled in vain to understand the basic estimates in Petrowsky’s paper [P1] on hyperbolic differential equations, but 40 years later they no longer seem so hard. We shall here discuss how this work of Petrowsky can in fact be easily understood from the point of view of pseudodifferential calculus for which it may be considered a crude precursor. For comparison we shall also present the original arguments of Petrowsky in a manner which we hope makes them more transparent.
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References
[H2] L. Hörmander, The analysis of linear partial differential operators I, Springer Verlag, 1983.
[H2] L. Hörmander, The analysis of linear partial differential operators III, Springer Verlag, 1985.
[P1] I, G. Petrowsky, Über das Cauchysche Problem für Systeme von partiellen Differentialgleichungen, Mat. Sb. 2(44) (1937), 815–870.
[P2] I, G. Petrowsky, Some remarks on my papers on the problem of Cauchy, Mat. Sb. 39(81) (1956), 267–272.
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Hörmander, L. (2018). Petrowsky’s L2 Estimates For Hyperbolic Systems. In: Unpublished Manuscripts . Springer, Cham. https://doi.org/10.1007/978-3-319-69850-2_4
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DOI: https://doi.org/10.1007/978-3-319-69850-2_4
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