Some recent quantitative unique continuation theorems

 Access to full text

 Full (PDF)

1. P. Anderson, Absence of diffusion in certain random lattices, Phys. Review 109 (1958) 1492–1505. 
2. B. Bollobas, Combinatorics, Cambridge U.P., 1986 MR866142
3. J. Bourgain, On localization for lattice Schrödinger operators involving Bernoulli variables, Lect. Notes Math., 1850 77–100, Springer Verlag, 2004. Zbl1083.35073MR2087153
4. J. Bourgain and C. Kenig, On localization in the Anderson-Bernoulli model in higher dimensions, Invent. Math. 161 (2005) 389–426. Zbl1084.82005MR2180453
5. T. Carleman, Sur un problème d’unicitè pour les systemes d’equations aux derivées portielles à deux variables indépendentes, Ark. for. Mat. 26B (1939) 1–9. Zbl0022.34201
6. R. Carmona, A. Klein and F. Martinelli, Anderson localization for Bernoulli and other singular potentials, Comm. Math. Phys. 108 (1987) 41–66. Zbl0615.60098MR872140
7. H. Donnelly and C. Fefferman, Nodol sets of eigenfunctions on Riemannian manifolds, Inv. Math. 93 (1988) 161–183. Zbl0659.58047MR943927
8. L. Escauriaza, F. J. Fernández and S. Vessella, Doubling Properties of coloric functions, to appear in Applicable Analysis. Zbl1090.35050
9. L. Escauriaza, C. Kenig, G. Ponce and L. Vega, Decay at infinity of caloric functions within characteristic hyperplanes, preprint. Zbl1116.35018
10. L. Escauriaza, C. Kenig, G. Ponce and L. Vega, On unique continuation of solutions of Schrödinger equations, preprint. Zbl1124.35068
11. L. Escauriaza, G. Seregin and V. Šverák, Backward uniqueness for parabolic equations, Arch. Rat. Mech. and Anal. 169 (2003) 147–157. Zbl1039.35052MR2005639
12. L. Escauriaza, G. Seregin and V. Šverák, Backward uniqueness for the least operator in half-space, St. Petersburg Math. J. 15 (2004) 139–148. Zbl1053.35052MR1979722
13. L. Escauriaza, G. Seregin and V. Šverák, $L^{3,\infty }$ solutions to the Navier-Stokes equations and backward uniqueness, Russ. Math. Surv. 58:2 (2003) 211–250. Zbl1064.35134MR1992563
14. J. Fröhlich, F. Martinelli, E. Scoppola and T. Spencer, Constructive proof of localization in the Anderson tight binding model, Comm. Math. Phys. 101 (1985) 21–46. Zbl0573.60096MR814541
15. J. Fröhlich and T. Spencer, Absence of diffusion with Anderson tight binding model for large disorder or low energy, Comm. Math. Phys. 88 (1983) 151–184. Zbl0519.60066MR696803
16. Y. Gol’dsheid, S. Molchanov and L. Pastur, Pure point spectrum of stochastic one dimensional Schrödinger operators, Funct. Anal. Appl. 11 (1977) 1–10. Zbl0368.34015
17. L. Hörmander, Uniqueness theorems for second order elliptic differential equations, Comm. PDE 8 (1983) 21–64. Zbl0546.35023MR686819
18. A. Ionescu and C. Kenig, $L^p$ Carleman inequalities and uniqueness of solutions of nonlinear Schrödinger equations, Acta Math. 193 (2004) 193–239. Zbl1209.35128MR2134866
19. A. Ionescu and C. Kenig, Uniqueness properties of solutions of Schrödinger equations, to appear, J. of Funct. Anal. Zbl1092.35104MR2200168
20. V. Isakov, Carleman type estimates in anisotrophic case and applications, J. Diff. Eqs 105 (1993) 217–238. Zbl0851.35028MR1240395
21. C. Kenig, G. Ponce and L. Vega, On unique continuation for the nonlinear Schrödinger equations, CPAM 60 (2002) 1247-1262. Zbl1041.35072MR1980854
22. V. A. Kondratiev and E. M. Landis, Quantitative theory of linear partial differential equations of second order, Encyclopedia of Math. Sci. 32 (Partial Differential Equations III), Springer-Verlag, Berlin 1988. Zbl0738.35006
23. E. M. Landis and O. A. Oleinik, Generalized analyticity and some related properties of solutions of elliptic and parabolic equations, Russian Math. Surv. 29 (1974) 195–212. Zbl0305.35014MR402268
24. V. Z. Meshkov, On the possible rate of decay at infinity of solutions of second order partial differential equations, Math. USSR Sbornik 72 (1992) 343–360. Zbl0782.35010MR1110071
25. L. Pastur and A. Figotin, Spectra of random and almost periodic operators, Heidelberg, Springer-Verlag 1992. Zbl0752.47002MR1223779
26. C. Shubin, R. Vakilian and T. Wolff, Some harmonic analysis questions suggested by Anderson-Bernoulli models, GAFA 8 (1988) 932–964. Zbl0920.42005MR1650106
27. E. M. Stein and R. Shakordin, Complex Analysis, Princeton Lectures in Analysis, Princeton University Press 2003. Zbl1020.30001MR1976398
28. F. Wegner, Bounds on the density of states in disordered systems, Z. Phys. B 44 (1981) 9–15. MR639135
29. B. Y. Zhang, Unique continuation for the nonlinear Schrödinger equation, Proc. Roy. Soc. Edinburgh Sect. A 127 (1997) 191–205. Zbl0879.35143MR1433092