Uniqueness properties of solutions of Schrödinger equations

Journal of Functional Analysis

Volumn 232, Issue 1, 2006, Pages 90-136

  Ionescu, Alexandru D ^a   Kenig, Carlos E ^b  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b UNIVERSITY OF CHICAGO   (United States)

Author keywords

Carleman inequalities; Local smoothing; Parametrices; Uniqueness of solutions

Indexed keywords

EID: 31044432932     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfa.2005.06.005     Document Type: Article

References (16)

1. J. Bourgain On the compactness of the support of solutions of dispersive equations Internat. Math. Res. Not. 1997 1997 437-447
2. L. Carleson On convergence and growth of partial sums of Fourier series Acta Math. 116 1966 135-157
3. P. Constantin J.C. Saut Local Smoothing properties of dispersive equations J. Amer. Math. Soc. 1 1988 413-439
4. p Carleman inequalities and uniqueness of solutions of nonlinear Schrödinger equations Acta Math. 193 2004 193-239
5. V. Isakov Carleman type estimates in an anisotropic case and applications J. Differential Equations 105 1993 217-238
6. D. Jerison Carleman inequalities for the Dirac and Laplace operators and unique continuation Adv. Math. 62 1986 118-134
7. C.E. Kenig G. Ponce L. Vega Smoothing effects and local existence theory for the generalized nonlinear Schrödinger equations Invent. Math. 134 1998 489-545
8. C.E. Kenig G. Ponce L. Vega On the support of solutions to the generalized KdV equation Ann. Inst. H. Poincaré Anal. Non Linéaire 19 2002 191-208
9. C.E. Kenig G. Ponce L. Vega On unique continuation for nonlinear Schrödinger equations Comm. Pure Appl. Math. 56 2003 1247-1262
10. C.E. Kenig G. Ponce L. Vega On the unique continuation of solutions to the generalized KdV equation Math. Res. Lett. 10 2003 833-846
11. C.E. Kenig, G. Ponce, L. Vega, On the uniqueness of solutions of higher order nonlinear dispersive equations, in: Inverse Problems: Theory and Applications (Cortona/Pisa, 2002) Contemporary Mathematics, vol. 333, American Mathematical Society, Providence, RI, 2003.
12. C.E. Kenig G. Ponce L. Vega The Cauchy problem for quasi-linear Schrödinger equations Invent. Math. 158 2004 343-388
13. P. Sjölin Regularity of solutions to the Schrödinger equations Duke Math. J. 55 1987 699-715
14. L. Vega Schrödinger equations: Pointwise convergence to the initial data Proc. Amer. Math. Soc. 102 1988 874-878
15. B.-Y. Zhang Unique continuation for the Korteweg-de Vries equation SIAM J. Math. Anal. 23 1992 55-71
16. B.-Y. Zhang Unique continuation properties of the nonlinear Schrödinger equation Proc. Roy. Soc. Edinburgh Sect. A 127 1997 191-205