Global estimates of fundamental solutions for higher-order Schrödinger equations

DOI10.1007/S00605-011-0350-0zbMath1256.35106arXiv1104.5367OpenAlexW2060192043MaRDI QIDQ1762466

Anton Arnold, Xiao Hua Yao, Jin-Myong Kim

Publication date: 27 November 2012

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1104.5367

zbMATH Keywords

oscillatory integralfundamental solution estimatehigher-order Schrödinger equation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Time-dependent Schrödinger equations and Dirac equations (35Q41) Harmonic analysis and PDEs (42B37)

Related Items (14)

Well-posedness of a higher-order Schrödinger-Poisson-Slater system ⋮ Normalized solutions of higher-order Schrödinger equations ⋮ Higher-order Schrödinger and Hartree–Fock equations ⋮ A note on the critical nonlinear high-order Schrödinger equation ⋮ Inhomogeneous oscillatory integrals and global smoothing effects for dispersive equations ⋮ Asymptotics for a class of oscillating fourth-order nonlinear Schrödinger equations ⋮ Dynamics of the nonlinear Klein-Gordon equation in the nonrelativistic limit ⋮ Estimates for a class of oscillatory integrals and decay rates for wave-type equations ⋮ Inhomogeneous nonlinear high-order evolution equations ⋮ Global and non-global solutions for a class of damped fourth-order Schrödinger equations ⋮ Probabilistic Approximation of the Solution of the Cauchy Problem for the Higher-Order Schrödinger Equation ⋮ Probabilistic approximation of the evolution operator \(e^{-itH}\) where \(H = \frac{( - 1)^m}{(2m)!} \frac{d^{2m}}{dx^{2m}}\) ⋮ Global well-posedness of some high-order focusing semilinear evolution equations with exponential nonlinearity ⋮ Decay estimates for higher-order elliptic operators

Cites Work

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• Pointwise estimates for a class of oscillatory integrals and related \(L^p\)--\(L^q\) estimates
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• \(L^p-L^q\) estimates for dispersive equations and related applications
• Convex hypersurfaces and \(L^p\) estimates for Schrödinger equations.
• Oscillatory integrals and \(L^p\) estimates for Schrödinger equations
• L p Estimates for Schrodinger Evolution Equations

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