Mizutani, Haruya Strichartz estimates for Schrödinger equations with variable coefficients and unbounded potentials. (English) Zbl 1297.35061 Anal. PDE 6, No. 8, 1857-1898 (2013). Summary: This paper is concerned with Schrödinger equations with variable coefficients and unbounded electromagnetic potentials, where the kinetic energy part is a long-range perturbation of the flat Laplacian and the electric (respectively magnetic) potential can grow subquadratically (respectively sublinearly) at spatial infinity. We prove sharp (local-in-time) Strichartz estimates, outside a large compact ball centered at the origin, for any admissible pair including the endpoint. Under the nontrapping condition on the Hamilton flow generated by the kinetic energy, global-in-space estimates are also studied. Finally, under the nontrapping condition, we prove Strichartz estimates with an arbitrarily small derivative loss without asymptotic flatness on the coefficients. Cited in 2 Documents MSC: 35B45 A priori estimates in context of PDEs 35Q41 Time-dependent Schrödinger equations and Dirac equations 35S30 Fourier integral operators applied to PDEs 81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory Keywords:asymptotically flat metric; long-range perturbation; nontrapping condition; small derivative loss PDF BibTeX XML Cite \textit{H. Mizutani}, Anal. PDE 6, No. 8, 1857--1898 (2013; Zbl 1297.35061) Full Text: DOI arXiv OpenURL References: This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.