Uniqueness in the Cauchy problems for higher order elliptic differential operators
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- by Wensheng Wang PDF
- Proc. Amer. Math. Soc. 126 (1998), 2623-2630 Request permission
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
- A.-P. Calderón, Uniqueness in the Cauchy problem for partial differential equations, Amer. J. Math. 80 (1958), 16–36. MR 104925, DOI 10.2307/2372819
- Christopher D. Sogge, Uniqueness in Cauchy problems for hyperbolic differential operators, Trans. Amer. Math. Soc. 333 (1992), no. 2, 821–833. MR 1066449, DOI 10.1090/S0002-9947-1992-1066449-1
- Wensheng Wang, Carleman inequalities and unique continuation for higher-order elliptic differential operators, Duke Math. J. 74 (1994), no. 1, 107–128. MR 1271465, DOI 10.1215/S0012-7094-94-07405-X
- T. H. Wolff, A property of measures in $\textbf {R}^N$ and an application to unique continuation, Geom. Funct. Anal. 2 (1992), no. 2, 225–284. MR 1159832, DOI 10.1007/BF01896975
Additional Information
- Wensheng Wang
- Affiliation: Department of Mathematics, Florida International University, Miami, Florida 33199
- Email: wangwens@zeus.fiu.edu, wangw@solix.fiu.edu
- Received by editor(s): May 27, 1993
- Communicated by: J. Marshall Ash
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 2623-2630
- MSC (1991): Primary 35Jxx
- DOI: https://doi.org/10.1090/S0002-9939-98-04707-8
- MathSciNet review: 1476397