The Log-effect for p-evolution type models

Massimo Cicognani; Fumihiko Hirosawa; Michael Reissig

doi:10.2969/jmsj/06030819

Journal of the Mathematical Society of Japan

Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645

The Log-effect for p-evolution type models

Massimo Cicognani, Fumihiko Hirosawa, Michael Reissig

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Keywords: Schrödinger equation, p-evolution model, non-regular coefficients, loss of regularity, well-posedness

JOURNAL FREE ACCESS

2008 Volume 60 Issue 3 Pages 819-863

DOI https://doi.org/10.2969/jmsj/06030819

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Abstract

The goal of the paper is to study the Log-effect for special p-evolution type models. The loss of regularity is related in an optimal way due to some unboundedness conditions for the derivatives of coefficients up to the second order with respect to t. Some counter-examples show that these conditions are sharp. We present the state of art of methods to construct such counter-examples.

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