Smoothness of solutions for Schrödinger equations with unbounded potentials

DOI10.2977/prims/1145475408zbMath1082.35054OpenAlexW2060391988MaRDI QIDQ2386886

Shin-ichi Doi

Publication date: 25 August 2005

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1145475408

zbMATH Keywords

well-posedenessscale of Sobolev spacesWeyl calculus techniques

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with quantum mechanics (35Q40) Initial value problems for linear higher-order PDEs (35G10)

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Transparent boundary conditions for iterative high-order parabolic equations, Strichartz estimates for Schrödinger equations with variable coefficients and potentials at most linear at spatial infinity, The Kato smoothing effect for regularized Schrödinger equations in exterior domains, Remark on the Kato Smoothing Effect for Schrödinger Equation with Superquadratic Potentials, L^p resolvent estimates for magnetic Schrödinger operators with unbounded background fields, Strichartz estimates for Schrödinger equations with variable coefficients and unbounded potentials. II: Superquadratic potentials, SPATIAL GROWTH OF FUNDAMENTAL SOLUTIONS FOR CERTAIN PERTURBATIONS OF THE HARMONIC OSCILLATOR, Semiclassical singularities propagation property for Schrödinger equations, Smoothing estimates for the Schrödinger equation with unbounded potentials, SCHRÖDINGER EQUATIONS WITH TIME-DEPENDENT UNBOUNDED SINGULAR POTENTIALS, Dispersion of singularities of solutions for Schrödinger equations, Kato Smoothing Effect for Schrödinger Operator

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