A unique continuation theorem for the Schrödinger equation with singular magnetic field
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- by Kazuhiro Kurata
- Proc. Amer. Math. Soc. 125 (1997), 853-860
- DOI: https://doi.org/10.1090/S0002-9939-97-03672-1
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Abstract:
We show a unique continuation theorem for the Schrödinger equation $(\frac {1}{i}\nabla -\mathbf {A})^2 u+ Vu=0$ with singular coefficients $\mathbf {A}$ and $V$.References
- B. Barceló, C. E. Kenig, A. Ruiz, and C. D. Sogge, Weighted Sobolev inequalities and unique continuation for the Laplacian plus lower order terms, Illinois J. Math. 32 (1988), no. 2, 230–245. MR 945861, DOI 10.1215/ijm/1255989128
- Michael S. P. Eastham and Hubert Kalf, Schrödinger-type operators with continuous spectra, Research Notes in Mathematics, vol. 65, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1982. MR 667015
- Eugene B. Fabes, Nicola Garofalo, and Fang-Hua Lin, A partial answer to a conjecture of B. Simon concerning unique continuation, J. Funct. Anal. 88 (1990), no. 1, 194–210. MR 1033920, DOI 10.1016/0022-1236(90)90125-5
- Nicola Garofalo and Fang-Hua Lin, Monotonicity properties of variational integrals, $A_p$ weights and unique continuation, Indiana Univ. Math. J. 35 (1986), no. 2, 245–268. MR 833393, DOI 10.1512/iumj.1986.35.35015
- Nicola Garofalo and Fang-Hua Lin, Unique continuation for elliptic operators: a geometric-variational approach, Comm. Pure Appl. Math. 40 (1987), no. 3, 347–366. MR 882069, DOI 10.1002/cpa.3160400305
- Hubert Kalf, Une remarque au sujet de prolongement unique des solutions de l’équation de Schrödinger, C. R. Acad. Sci. Paris Sér. I Math. 295 (1982), no. 10, 579–581 (French, with English summary). MR 685029
- Lars Hörmander, Uniqueness theorems for second order elliptic differential equations, Comm. Partial Differential Equations 8 (1983), no. 1, 21–64. MR 686819, DOI 10.1080/03605308308820262
- Kazuhiro Kurata, A unique continuation theorem for uniformly elliptic equations with strongly singular potentials, Comm. Partial Differential Equations 18 (1993), no. 7-8, 1161–1189. MR 1233189, DOI 10.1080/03605309308820968
- Kurata, K. Local boundedness and continuity for weak solutions of $-(\nabla - i{ \mathbf {b}})^2 u+ Vu=0$. Math. Z. (to appear).
- Christopher D. Sogge, Strong uniqueness theorems for second order elliptic differential equations, Amer. J. Math. 112 (1990), no. 6, 943–984. MR 1081811, DOI 10.2307/2374732
- Thomas H. Wolff, Unique continuation for $|\Delta u|\le V|\nabla u|$ and related problems, Rev. Mat. Iberoamericana 6 (1990), no. 3-4, 155–200. MR 1125760, DOI 10.4171/RMI/101
- 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
Bibliographic Information
- Kazuhiro Kurata
- Affiliation: Department of Mathematics, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji-shi, Tokyo, 192-03 Japan
- Email: kurata@math.metro-u.ac.jp
- Received by editor(s): April 3, 1995
- Received by editor(s) in revised form: October 3, 1995
- Communicated by: Christopher D. Sogge
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 853-860
- MSC (1991): Primary 35B60, 35J10, 35Q60
- DOI: https://doi.org/10.1090/S0002-9939-97-03672-1
- MathSciNet review: 1363173