Mathematische Annalen

, Volume 315, Issue 4, pp 529–567

Gain of regularity for semilinear Schrödinger equations

  • Hiroyuki Chihara
Original article

DOI: 10.1007/s002080050328

Cite this article as:
Chihara, H. Math Ann (1999) 315: 529. doi:10.1007/s002080050328

Abstract.

We discuss local existence and gain of regularity for semilinear Schrödinger equations which generally cause loss of derivatives. We prove our results by advanced energy estimates. More precisely, block diagonalization and Doi's transformation, together with symbol smoothing for pseudodifferential operators with nonsmooth coefficients, apply to systems of Schrödinger-type equations. In particular, the sharp Gårding inequality for pseudodifferential operators whose coefficients are twice continuously differentiable, plays a crucial role in our proof.

Mathematics Subject Classification (1991):35Q55, 35B65, 35G25, 35S05

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Hiroyuki Chihara
    • 1
  1. 1.Department of Mathematical Sciences, Shinshu University, Matsumoto 390-8621, Japan (e-mail: chihara@math.shinshu-u.ac.jp) JP