On the boundary convergence of solutions to the Hermite-Schrödinger equation

• Autorzy: Peter Sjögren , J. L. Torrea
• Języki publikacji: EN

Abstrakty

EN

In the half-space $ℝ^{d} × ℝ₊$, consider the Hermite-Schrödinger equation i∂u/∂t = -Δu + |x|²u, with given boundary values on $ℝ^{d}$. We prove a formula that links the solution of this problem to that of the classical Schrödinger equation. It shows that mixed norm estimates for the Hermite-Schrödinger equation can be obtained immediately from those known in the classical case. In one space dimension, we deduce sharp pointwise convergence results at the boundary by means of this link.

Kategorie tematyczne

• 42B35: Function spaces arising in harmonic analysis
• 42B37: Harmonic analysis and PDE
• 35K15: Initial value problems for second-order parabolic equations
• 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2010
• Tom: 118
• Numer: 1
• Strony: 161-174

Daty

wydano

2010

Twórcy

autor

Peter Sjögren

• Mathematical Sciences, University of Gothenburg, SE-412 96 Göteborg, Sweden
• Mathematical Sciences, Chalmers, SE-412 96 Göteborg, Sweden

autor

J. L. Torrea

• Departamento de Matemáticas, and ICMAT CSIC-UAM-UCM-UC3M, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain

Identyfikatory

DOI

10.4064/cm118-1-8