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A note on unique continuation for Schrödinger's operator
Authors:
Carlos E. Kenig and Christopher D. Sogge
Journal:
Proc. Amer. Math. Soc. 103 (1988), 543-546
MSC:
Primary 35J10; Secondary 35B45
MathSciNet review:
943081
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Abstract: In this paper we shall prove a unique continuation theorem for Schrödinger's operator, . This will be a consequence of "uniform Sobolev inequalities" for operators which are the Schrödinger operator plus lower order terms in .
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Hörmander, Uniqueness theorems for second order elliptic
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C.
E. Kenig, A.
Ruiz, and C.
D. Sogge, Uniform Sobolev inequalities and unique continuation for
second order constant coefficient differential operators, Duke Math.
J. 55 (1987), no. 2, 329–347. MR 894584
(88d:35037), http://dx.doi.org/10.1215/S0012-7094-87-05518-9
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(58 #23577)
- [1]
- L. Hörmander, Uniqueness theorems for second-order elliptic differential operators, Comm. Partial Differential Equations 8 (1983), 21-64. MR 686819 (85c:35018)
- [2]
- D. Jerison and C. E. Kenig, Unique continuation and absence of positive eigenvalues for Schrödinger operators, Ann. of Math. 121 (1985), 463-494. MR 794370 (87a:35058)
- [3]
- C. E. Kenig, A. Ruiz, and C. D. Sogge, Uniform Sobolev inequalities and unique continuation theorems for second-order constant coefficient differential operators, Duke Math. J. 55 (1987), 329-347. MR 894584 (88d:35037)
- [4]
- R. S. Strichartz, A priori estimates for the wave equation and some applications, J. Funct. Anal. 5 (1970), 218-235. MR 0257581 (41:2231)
- [5]
- -, Restrictions of Fourier transforms to quadratic surfaces, Duke Math. J. 44 (1977), 705-714. MR 0512086 (58:23577)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9939-1988-0943081-3
PII:
S 0002-9939(1988)0943081-3
Keywords:
Sobolev inequalities,
unique continuation,
restriction theorems
Article copyright:
© Copyright 1988 American Mathematical Society
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