Unique continuation for the Schrödinger equation with gradient vector potentials
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- by Hongjie Dong and Wolfgang Staubach PDF
- Proc. Amer. Math. Soc. 135 (2007), 2141-2149 Request permission
Abstract:
We obtain unique continuation results for Schrödinger equations with time dependent gradient vector potentials. This result with an appropriate modification also yields unique continuation properties for solutions of certain nonlinear Schrödinger equations.References
- Jean Bourgain, On the compactness of the support of solutions of dispersive equations, Internat. Math. Res. Notices 9 (1997), 437–447. MR 1443322, DOI 10.1155/S1073792897000305
- L. Escauriaza, C.E. Kenig, G. Ponce, L. Vega, On unique continuation of solutions of Schrödinger equations, to appear in Comm. PDE.
- L. Escauriaza, C.E. Kenig, G. Ponce, L. Vega, On uniqueness properties of solutions of the $k-$generalized KdV equations, preprint.
- Carlos E. Kenig, Gustavo Ponce, and Luis Vega, Smoothing effects and local existence theory for the generalized nonlinear Schrödinger equations, Invent. Math. 134 (1998), no. 3, 489–545. MR 1660933, DOI 10.1007/s002220050272
- Alexandru D. Ionescu and Carlos E. Kenig, $L^p$ Carleman inequalities and uniqueness of solutions of nonlinear Schrödinger equations, Acta Math. 193 (2004), no. 2, 193–239. MR 2134866, DOI 10.1007/BF02392564
- Alexandru D. Ionescu and Carlos E. Kenig, Uniqueness properties of solutions of Schrödinger equations, J. Funct. Anal. 232 (2006), no. 1, 90–136. MR 2200168, DOI 10.1016/j.jfa.2005.06.005
- Carlos E. Kenig, Gustavo Ponce, and Luis Vega, On unique continuation for nonlinear Schrödinger equations, Comm. Pure Appl. Math. 56 (2003), no. 9, 1247–1262. MR 1980854, DOI 10.1002/cpa.10094
- Carlos E. Kenig, Gustavo Ponce, and Luis Vega, The Cauchy problem for quasi-linear Schrödinger equations, Invent. Math. 158 (2004), no. 2, 343–388. MR 2096797, DOI 10.1007/s00222-004-0373-4
Additional Information
- Hongjie Dong
- Affiliation: School of Mathematics, Institute for Advanced Study, 1 Einstein Drive, Princeton, New Jersey 08540
- MR Author ID: 761067
- ORCID: 0000-0003-2258-3537
- Email: hjdong@ias.edu
- Wolfgang Staubach
- Affiliation: Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, Illinois 60637
- MR Author ID: 675031
- Email: wolf@math.uchicago.edu
- Received by editor(s): March 18, 2006
- Published electronically: March 2, 2007
- Communicated by: David S. Tartakoff
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 2141-2149
- MSC (2000): Primary 35B37
- DOI: https://doi.org/10.1090/S0002-9939-07-08813-2
- MathSciNet review: 2299492