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.
Publié le : 2008-07-15
Classification:
Schrödinger equation,
p-evolution model,
non-regular coefficients,
loss of regularity,
well-posedness,
35L05,
35L15,
35Q40
@article{1217884494,
author = {CICOGNANI, Massimo and HIROSAWA, Fumihiko and REISSIG, Michael},
title = {The Log-effect for p-evolution type models},
journal = {J. Math. Soc. Japan},
volume = {60},
number = {1},
year = {2008},
pages = { 819-863},
language = {en},
url = {http://dml.mathdoc.fr/item/1217884494}
}
CICOGNANI, Massimo; HIROSAWA, Fumihiko; REISSIG, Michael. The Log-effect for p-evolution type models. J. Math. Soc. Japan, Tome 60 (2008) no. 1, pp. 819-863. http://gdmltest.u-ga.fr/item/1217884494/