UnivTrevesV1, Main, Exploration, bibRecord, 001602

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

Identifieur interne : 001602 ( Main/Exploration ); précédent : 001601; suivant : 001603

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

Source :

RBID : Hal:hal-00016103

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 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.

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https://hal.archives-ouvertes.fr/hal-00016103

Affiliations:

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Le document en format XML

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<front><div type="abstract" xml:lang="en">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.</div>
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Cutting the loss of derivatives for solvability under condition (psi)

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

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Abstract

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