Unique continuation for the Schrödinger equation with gradient vector potentials

DOI10.1090/S0002-9939-07-08813-2zbMath1119.35083arXivmath/0603443OpenAlexW2002514482MaRDI QIDQ3432776

Wolfgang Staubach, Hongjie Dong

Publication date: 18 April 2007

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0603443

zbMATH Keywords

uniquenessinitial-value problemCarleman estimates

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Continuation and prolongation of solutions to PDEs (35B60)

Related Items (6)

The sharp Hardy uncertainty principle for Schrödinger evolutions ⋮ On unique continuation for the generalized Schrödinger equations ⋮ Unique continuation for the Schrödinger equation with gradient term ⋮ Uniqueness properties of solutions to Schrödinger equations ⋮ Hardy uncertainty principle, convexity and parabolic evolutions ⋮ Sharp Hardy uncertainty principle and gaussian profiles of covariant Schrödinger evolutions

Cites Work

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• \(L^p\) Carleman inequalities and uniqueness of solutions of nonlinear Schrödinger equations
• Unique continuation for Schrödinger evolutions, with applications to profiles of concentration and traveling waves
• The Cauchy problem for quasi-linear Schrödinger equations
• On uniqueness properties of solutions of the \(k\)-generalized KdV equations
• Smoothing effects and local existence theory for the generalized nonlinear Schrödinger equations
• Uniqueness properties of solutions of Schrödinger equations
• On unique continuation for nonlinear Schrödinger equations

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