Cutting the loss of derivatives for solvability under condition ( Ψ )

Nicolas Lerner

Bulletin de la Société Mathématique de France (2006)

  • Volume: 134, Issue: 4, page 559-631
  • ISSN: 0037-9484

Abstract

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For a principal type pseudodifferential operator, we prove that condition  ( ψ ) implies local solvability with a loss of 3/2 derivatives. We use many elements of Dencker’s paper on the proof of the Nirenberg-Treves conjecture and we provide some improvements of the key energy estimates which allows us to cut the loss of derivatives from ϵ + 3 / 2 for any ϵ > 0 (Dencker’s most recent result) to 3/2 (the present paper). It is already known that condition  ( ψ ) doesnotimply local solvability with a loss of 1 derivative, so we have to content ourselves with a loss > 1 .

How to cite

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Lerner, Nicolas. "Cutting the loss of derivatives for solvability under condition $(\Psi )$." Bulletin de la Société Mathématique de France 134.4 (2006): 559-631. <http://eudml.org/doc/272406>.

@article{Lerner2006,
abstract = {For a principal type pseudodifferential operator, we prove that condition $(\psi )$ implies local solvability with a loss of 3/2 derivatives. We use many elements of Dencker’s paper on the proof of the Nirenberg-Treves conjecture and we provide some improvements of the key energy estimates which allows us to cut the loss of derivatives from $\epsilon +3/2$ for any $\epsilon &gt;0$ (Dencker’s most recent result) to 3/2 (the present paper). It is already known that condition $(\psi )$ doesnotimply local solvability with a loss of 1 derivative, so we have to content ourselves with a loss $&gt;1$.},
author = {Lerner, Nicolas},
journal = {Bulletin de la Société Mathématique de France},
keywords = {solvability; a priori estimates; pseudodifferential operators},
language = {eng},
number = {4},
pages = {559-631},
publisher = {Société mathématique de France},
title = {Cutting the loss of derivatives for solvability under condition $(\Psi )$},
url = {http://eudml.org/doc/272406},
volume = {134},
year = {2006},
}

TY - JOUR
AU - Lerner, Nicolas
TI - Cutting the loss of derivatives for solvability under condition $(\Psi )$
JO - Bulletin de la Société Mathématique de France
PY - 2006
PB - Société mathématique de France
VL - 134
IS - 4
SP - 559
EP - 631
AB - For a principal type pseudodifferential operator, we prove that condition $(\psi )$ implies local solvability with a loss of 3/2 derivatives. We use many elements of Dencker’s paper on the proof of the Nirenberg-Treves conjecture and we provide some improvements of the key energy estimates which allows us to cut the loss of derivatives from $\epsilon +3/2$ for any $\epsilon &gt;0$ (Dencker’s most recent result) to 3/2 (the present paper). It is already known that condition $(\psi )$ doesnotimply local solvability with a loss of 1 derivative, so we have to content ourselves with a loss $&gt;1$.
LA - eng
KW - solvability; a priori estimates; pseudodifferential operators
UR - http://eudml.org/doc/272406
ER -

References

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