Carleman inequalities for the Dirac operator and strong unique continuation
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- by Yonne Mi Kim
- Proc. Amer. Math. Soc. 123 (1995), 2103-2112
- DOI: https://doi.org/10.1090/S0002-9939-1995-1242093-6
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Abstract:
Using a Carleman inequality, we prove a strong unique continuation theorem for the Schrödinger operator $D + V$, where D is the Dirac operator and V is a potential function in some ${L^p}$ space.References
- S. Alinhac and M. S. Baouendi, Uniqueness for the characteristic Cauchy problem and strong unique continuation for higher order partial differential inequalities, Amer. J. Math. 102 (1980), no. 1, 179–217. MR 556891, DOI 10.2307/2374175 T. Carleman, Sur un problèm d’unicité pour les systèmes d’èquations aux derivées partielles à deux variables indépendantes, Ark. Mat. 26B (1939), 1-9.
- Lars Hörmander, Uniqueness theorems for second order elliptic differential equations, Comm. Partial Differential Equations 8 (1983), no. 1, 21–64. MR 686819, DOI 10.1080/03605308308820262
- David Jerison, Carleman inequalities for the Dirac and Laplace operators and unique continuation, Adv. in Math. 62 (1986), no. 2, 118–134. MR 865834, DOI 10.1016/0001-8708(86)90096-4
- David Jerison and Carlos E. Kenig, Unique continuation and absence of positive eigenvalues for Schrödinger operators, Ann. of Math. (2) 121 (1985), no. 3, 463–494. With an appendix by E. M. Stein. MR 794370, DOI 10.2307/1971205 C. E. Kenig, Uniform Sobolev inequalities for second order differential operators and unique continuation theorem, Internat. Congr. Math., 1986.
- Barry Simon, Schrödinger semigroups, Bull. Amer. Math. Soc. (N.S.) 7 (1982), no. 3, 447–526. MR 670130, DOI 10.1090/S0273-0979-1982-15041-8
- Christopher D. Sogge, Oscillatory integrals and spherical harmonics, Duke Math. J. 53 (1986), no. 1, 43–65. MR 835795, DOI 10.1215/S0012-7094-86-05303-2
- Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095 M. E. Taylor, Pseudo differential operators, Princeton Univ. Press, Princeton, NJ, 1981.
- Peter A. Tomas, A restriction theorem for the Fourier transform, Bull. Amer. Math. Soc. 81 (1975), 477–478. MR 358216, DOI 10.1090/S0002-9904-1975-13790-6
- Thomas H. Wolff, Note on counterexamples in strong unique continuation problems, Proc. Amer. Math. Soc. 114 (1992), no. 2, 351–356. MR 1014648, DOI 10.1090/S0002-9939-1992-1014648-2
Bibliographic Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 2103-2112
- MSC: Primary 35B60; Secondary 35Q40
- DOI: https://doi.org/10.1090/S0002-9939-1995-1242093-6
- MathSciNet review: 1242093