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arXiv: math.AP/0512455

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

Nicolas Lerner 1

(2005-12-19)

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 2 (Dencker's result) to 3/2 (the present paper). It is already known that condition (psi) does not imply local solvability with a loss of 1 derivative, so we have to content ourselves with a loss >1.

1:	Institut de Recherche Mathématique de Rennes (IRMAR)
	CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne

Subject

:

Mathematics/Analysis of PDEs

Keyword(s): solvability – pseudodifferential operators

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From: Nicolas Lerner <>

Submitted on: Monday, 19 December 2005 16:09:24

Updated on: Tuesday, 23 March 2010 13:44:15