Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

A unique continuation theorem for the Schrödinger equation with singular magnetic field

Author(s): Kazuhiro Kurata
Journal: Proc. Amer. Math. Soc. 125 (1997), 853-860.
MSC (1991): Primary 35B60, 35J10, 35Q60
MathSciNet review: 1363173
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

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:

[BKRS]: Barcelo, B., Kenig, C. E., Ruiz, A., Sogge, C. D. Weighted Sobolev inequalities and unique continuation for the Laplacian plus lower order terms. Illinois J.Math. 32(1988), 230-245. MR 89h:35048
[EK]: Eastham, M. S. P., Kalf, H. Schrödinger-type operators with continuous spectra. Pitman Lecture Note Series 65, Longman. MR 84i:35107
[FGL]: Fabes, E. B., Garofalo, N., Lin, F. H. A partial answer to a conjecture of B.Simon concerning unique continuation. J. Fun. Ana. 88(1990), 194-210. MR 91m:35074
[GL1]: Garofalo, N., Lin, F. H. Monotonicity properties of variational integrals, weights and unique continuation. Indiana Univ. Math. J. 35(1986), 245-268. MR 88b:35059
[GL2]: Garofalo, N., Lin, F. H. Unique continuation for elliptic operators: A geometric-variational approach. Comm. Pure Appl. Math. 40(1987), 347-366. MR 88j:35046
[Ka]: Kalf, H. Une remarque au sujet de prolongement unique des solutions de l'équation de Schrödinger. C.R. Acad. Sc. Paris, 295(1982), 579-581. MR 84f:35032
[H]: Hörmander, L. Uniqueness theorems for second-order elliptic differential equations. Comm. in P.D.E. 8(1983), 21-64. MR 85c:35018
[Ku1]: Kurata, K. A unique continuation theorem for uniformly elliptic equations with strongly singular potentials. Comm. in P.D.E. 18(7& 8) (1993), 1161-1189. MR 95b:35034
[Ku2]: Kurata, K. Local boundedness and continuity for weak solutions of $-(\nabla - i{ \mathbf {b}})^2 u+ Vu=0$ . Math. Z. (to appear).
[So]: Sogge, C. D. Strong uniqueness theorems for second order elliptic differential equations. Amer. J. Math. 112(1990), 943-984. MR 91k:35068
[Wo1]: Wolff, T. H. Unique continuation for $|\Delta u| \le V|\nabla u|$ and related problems. Revista Math. Iberoamericana 6(1990), 155-200. MR 93a:35061
[Wo2]: Wolff, T. H. A property of measures in ${ \mathbf {R}}^n$ and an application to unique continuation. Geometric and Fun. Ana. 2, No. 2 (1992), 225-284. MR 93c:35015

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|