On a unique continuation for Aharonov-Bohm magnetic Schrödinger equation. (English) Zbl 1379.35045
Summary: We furnish a unique continuation for a suitable two-dimensional magnetic Schrödinger equation defined on the complement of a compact set.
MSC:
| 35B60 | Continuation and prolongation of solutions to PDEs |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35J10 | Schrödinger operator, Schrödinger equation |
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
References:
| [1] | J. Cruz-Sampedro, Unique continuation at infinity of solutions to Schrödinger equations with complex-valued potentials, Proc. Edinb. Math. Soc. (2) 42 (1999), no. 1, 143-153.; Cruz-Sampedro, J., Unique continuation at infinity of solutions to Schrödinger equations with complex-valued potentials, Proc. Edinb. Math. Soc. (2), 42, 1, 143-153 (1999) · Zbl 0941.35016 |
| [2] | A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, Comm. Pure Appl. Math. 12 (1959), 623-727.; Douglis, A.; Nirenberg, L., Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, Comm. Pure Appl. Math., 12, 623-727 (1959) · Zbl 0093.10401 |
| [3] | R. Froese, I. Herbest, M. Hoffman-Ostenhoff and T. Hoffman-Ostenhoff, \(L^2\)-lower bounds to solutions of one-body Schrödinger equations, Proc. Roy. Soc. Edinburgh Sect. A 95 (1983), no. 1-2, 25-38.; Froese, R.; Herbest, I.; Hoffman-Ostenhoff, M.; Hoffman-Ostenhoff, T., \(L^2\)-lower bounds to solutions of one-body Schrödinger equations, Proc. Roy. Soc. Edinburgh Sect. A, 95, 1-2, 25-38 (1983) · Zbl 0547.35038 |
| [4] | L. Hörmander, The Analysis of Linear Partial Differential Operators. Vol. II, Springer, Berlin, 1985.; Hörmander, L., The Analysis of Linear Partial Differential Operators. Vol. II (1985) · Zbl 0601.35001 |
| [5] | V. A. Kondratiev and E. M. Landis, Qualitative theory of second order partial differential equations, Partial Differential Equations III: The Cauchy Problem. Qualitative Theory of Partial Differential Equations, Encyclopaedia Math. Sci. 32, Springer, Berlin (1991), 87-192.; Kondratiev, V. A.; Landis, E. M., Qualitative theory of second order partial differential equations, Partial Differential Equations III: The Cauchy Problem. Qualitative Theory of Partial Differential Equations, 87-192 (1991) · Zbl 0738.35006 |
| [6] | V. Z. Meshkov, On the possible Rate of decay at infinity of solutions of second order partial differential equations, Math. USSR Sb. 72 (1992), no. 2, 343-361.; Meshkov, V. Z., On the possible Rate of decay at infinity of solutions of second order partial differential equations, Math. USSR Sb., 72, 2, 343-361 (1992) · Zbl 0782.35010 |
| [7] | M. Reed and B. Simon, Methods of Modern Mathematical Physics. Vol. 4, Academic Press, New York, 1978.; Reed, M.; Simon, B., Methods of Modern Mathematical Physics. Vol. 4 (1978) · Zbl 0401.47001 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
