On unique continuation for Schrödinger operators of fractional and higher orders
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Publication:5417584
DOI10.1002/mana.201300008zbMath1290.35315arXiv1301.2460OpenAlexW1606259493MaRDI QIDQ5417584
Publication date: 21 May 2014
Published in: Mathematische Nachrichten (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1301.2460
Schrödinger operator, Schrödinger equation (35J10) Continuation and prolongation of solutions to PDEs (35B60) Fractional partial differential equations (35R11)
Related Items (12)
Strong unique continuation and local asymptotics at the boundary for fractional elliptic equations ⋮ On quantitative unique continuation properties of fractional Schrödinger equations: Doubling, vanishing order and nodal domain estimates ⋮ Strict monotonicity and unique continuation for general non-local eigenvalue problems ⋮ Zero-energy bound state decay for non-local Schrödinger operators ⋮ Unique continuation and classification of blow-up profiles for elliptic systems with Neumann boundary coupling and applications to higher order fractional equations ⋮ Unique continuation for fractional Schrödinger operators in three and higher dimensions ⋮ Strong unique continuation for the higher order fractional Laplacian ⋮ Potentials for non-local Schrödinger operators with zero eigenvalues ⋮ Absence of embedded eigenvalues for non-local Schrödinger operators ⋮ Unique Continuation for Fractional Schrödinger Equations with Rough Potentials ⋮ Unique continuation principles for a higher order fractional Laplace equation ⋮ On the Calderón problem for nonlocal Schrödinger equations with homogeneous, directionally antilocal principal symbols
Cites Work
- Unique continuation for Schrödinger operators in dimension three or less
- A partial answer to a conjecture of B. Simon concerning unique continuation
- Unique continuation and absence of positive eigenvalues for Schrödinger operators. (With an appendix by E. M. Stein)
- Fractional quantum mechanics and Lévy path integrals
- Remark on unique continuation for higher powers of the Laplace operator
- Schrödinger operators with singular potentials
- Sharp counterexamples in unique continuation for second order elliptic equations
- Schrödinger semigroups
- Unique continuation for Schrödinger operators and for higher powers of the Laplacian
- Higher-order Kato class potentials for Schrödinger operators
- On the behavior of the solutions of the differential equation ΔU = F(x,u) in the neighborhood of a point
- A counterexample in unique continuation
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