Gain of regularity for semilinear Schrödinger equations |
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Authors: | Hiroyuki Chihara |
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Institution: | (1) Department of Mathematical Sciences, Shinshu University, Matsumoto 390-8621, Japan (e-mail: chihara@math.shinshu-u.ac.jp) , JP |
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Abstract: | We discuss local existence and gain of regularity for semilinear Schr?dinger 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 Schr?dinger-type equations.
In particular, the sharp G?rding inequality for pseudodifferential operators whose coefficients are twice continuously differentiable,
plays a crucial role in our proof.
Received: 14 December 1998 |
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Keywords: | Mathematics Subject Classification (1991):35Q55 35B65 35G25 35S05 |
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