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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Uniqueness in the Cauchy problems for higher order elliptic differential operators

Author(s): Wensheng Wang
Journal: Proc. Amer. Math. Soc. 126 (1998), 2623-2630.
MSC (1991): Primary 35Jxx
MathSciNet review: 1476397
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Abstract | References | Similar articles | Additional information

Abstract: In this note, we study the uniqueness in Cauchy problems for a class of higher order elliptic differential operators with Lipschitz coefficients. In particular, we prove the uniqueness under assuming the potentials being $L^{r_{j}}_{ \text{loc}}$ with certain correct numbers $r_{j}$'s.


References:

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A. P. Calderon, Uniqueness in the Cauchy problem for partial differential equations, Amer. J. Math., 80 (1958) 16-36. MR 21:3675

2.
C. Sogge, Uniqueness in Cauchy problem for hyperbolic differential operator, Trans. of AMS., 333 (1992) 821-833. MR 92m:35006

3.
W. Wang, Carleman inequalities and unique continuation for higher order elliptic differential operators, Duke Math. J., 74 (1994) 107-128. MR 95j:35078

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T. Wolff, A property of measures in $R^{n}$ and an application to unique continuation, Geometrical and Functional Analysis, 2 (1992) 225-284. MR 93c:35015


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Additional Information:

Wensheng Wang
Affiliation: Department of Mathematics, Florida International University, Miami, Florida 33199
Email: wangwens@zeus.fiu.edu, wangw@solix.fiu.edu

DOI: 10.1090/S0002-9939-98-04707-8
PII: S 0002-9939(98)04707-8
Received by editor(s): May 27, 1993
Communicated by: J. Marshall Ash
Copyright of article: Copyright 1998, American Mathematical Society




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