Some recent quantitative unique continuation theorems
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2005-2006), Exposé no. 20, 10 p.
Kenig, Carlos E. 1

1 Department of Mathematics University of Chicago Chicago, IL 60637 USA
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Kenig, Carlos E. Some recent quantitative unique continuation theorems. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2005-2006), Exposé no. 20, 10 p. http://www.numdam.org/item/SEDP_2005-2006____A20_0/

[A] P. Anderson, Absence of diffusion in certain random lattices, Phys. Review 109 (1958) 1492–1505.

[Bo] B. Bollobas, Combinatorics, Cambridge U.P., 1986 | MR

[B] J. Bourgain, On localization for lattice Schrödinger operators involving Bernoulli variables, Lect. Notes Math., 1850 77–100, Springer Verlag, 2004. | MR | Zbl

[B-K] J. Bourgain and C. Kenig, On localization in the Anderson-Bernoulli model in higher dimensions, Invent. Math. 161 (2005) 389–426. | MR | Zbl

[C] 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. | Zbl

[C-K-M] R. Carmona, A. Klein and F. Martinelli, Anderson localization for Bernoulli and other singular potentials, Comm. Math. Phys. 108 (1987) 41–66. | MR | Zbl

[D-F] H. Donnelly and C. Fefferman, Nodol sets of eigenfunctions on Riemannian manifolds, Inv. Math. 93 (1988) 161–183. | MR | Zbl

[E-F-V] L. Escauriaza, F. J. Fernández and S. Vessella, Doubling Properties of coloric functions, to appear in Applicable Analysis. | Zbl

[E-K-P-V 1] L. Escauriaza, C. Kenig, G. Ponce and L. Vega, Decay at infinity of caloric functions within characteristic hyperplanes, preprint. | Zbl

[E-K-P-V 2] L. Escauriaza, C. Kenig, G. Ponce and L. Vega, On unique continuation of solutions of Schrödinger equations, preprint. | Zbl

[E-S-S 1] L. Escauriaza, G. Seregin and V. Šverák, Backward uniqueness for parabolic equations, Arch. Rat. Mech. and Anal. 169 (2003) 147–157. | MR | Zbl

[E-S-S 2] L. Escauriaza, G. Seregin and V. Šverák, Backward uniqueness for the least operator in half-space, St. Petersburg Math. J. 15 (2004) 139–148. | MR | Zbl

[E-S-S 3] L. Escauriaza, G. Seregin and V. Šverák, L 3, solutions to the Navier-Stokes equations and backward uniqueness, Russ. Math. Surv. 58:2 (2003) 211–250. | MR | Zbl

[F-M-S-S] 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. | MR | Zbl

[F-S] 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. | MR | Zbl

[G-M-P] Y. Gol’dsheid, S. Molchanov and L. Pastur, Pure point spectrum of stochastic one dimensional Schrödinger operators, Funct. Anal. Appl. 11 (1977) 1–10. | Zbl

[H] L. Hörmander, Uniqueness theorems for second order elliptic differential equations, Comm. PDE 8 (1983) 21–64. | MR | Zbl

[I-K 1] A. Ionescu and C. Kenig, L p Carleman inequalities and uniqueness of solutions of nonlinear Schrödinger equations, Acta Math. 193 (2004) 193–239. | MR | Zbl

[I-K 2] A. Ionescu and C. Kenig, Uniqueness properties of solutions of Schrödinger equations, to appear, J. of Funct. Anal. | MR | Zbl

[I] V. Isakov, Carleman type estimates in anisotrophic case and applications, J. Diff. Eqs 105 (1993) 217–238. | MR | Zbl

[K-P-V] C. Kenig, G. Ponce and L. Vega, On unique continuation for the nonlinear Schrödinger equations, CPAM 60 (2002) 1247-1262. | MR | Zbl

[K-L] 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. | Zbl

[L-O] 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. | MR | Zbl

[M] 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. | MR | Zbl

[P-F] L. Pastur and A. Figotin, Spectra of random and almost periodic operators, Heidelberg, Springer-Verlag 1992. | MR | Zbl

[S-V-W] C. Shubin, R. Vakilian and T. Wolff, Some harmonic analysis questions suggested by Anderson-Bernoulli models, GAFA 8 (1988) 932–964. | MR | Zbl

[S-S] E. M. Stein and R. Shakordin, Complex Analysis, Princeton Lectures in Analysis, Princeton University Press 2003. | MR | Zbl

[We] F. Wegner, Bounds on the density of states in disordered systems, Z. Phys. B 44 (1981) 9–15. | MR

[Z] B. Y. Zhang, Unique continuation for the nonlinear Schrödinger equation, Proc. Roy. Soc. Edinburgh Sect. A 127 (1997) 191–205. | MR | Zbl