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Uniqueness in Cauchy problems for hyperbolic differential operators


Author: Christopher D. Sogge
Journal: Trans. Amer. Math. Soc. 333 (1992), 821-833
MSC: Primary 35A05; Secondary 35B60, 35L25
DOI: https://doi.org/10.1090/S0002-9947-1992-1066449-1
MathSciNet review: 1066449
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Abstract: In this paper we prove a unique continuation theorem for second order strictly hyperbolic differential operators. Results also hold for higher order operators if the hyperbolic cones are strictly convex. These results are proved via certain Carleman inequalities. Unlike [6], the parametrices involved only have real phase functions, but they also have Gaussian factors. We estimate the parametrices and associated remainders using sharp $ {L^p}$ estimates for Fourier integral operators which are due to Brenner [1] and Seeger, Stein, and the author [5].


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DOI: https://doi.org/10.1090/S0002-9947-1992-1066449-1
Article copyright: © Copyright 1992 American Mathematical Society

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