For a principal type pseudodifferential operator, we prove that condition 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 for any (Dencker’s most recent result) to 3/2 (the present paper). It is already known that condition does not imply local solvability with a loss of 1 derivative, so we have to content ourselves with a loss .
Pour un opérateur de type principal, nous démontrons que la condition () implique la résolubilité locale avec perte de 3/2 dérivées. Nous utilisons beaucoup d’éléments de la démonstration par Dencker de la conjecture de Nirenberg-Treves et nous limitons la perte de dérivées à 3/2, améliorant le résultat le plus récent de Dencker (perte de dérivées pour tout ). La condition () n’impliquant pas la résolubilité locale avec perte d’une dérivée, nous devons nous contenter d’une perte .
Keywords: solvability, a priori estimates, pseudodifferential operators
Mot clés : résolubilité, estimations a priori, op´erateurs pseudodifférentiels
@article{BSMF_2006__134_4_559_0, author = {Lerner, Nicolas}, title = {Cutting the loss of derivatives for solvability under condition $(\Psi )$}, journal = {Bulletin de la Soci\'et\'e Math\'ematique de France}, pages = {559--631}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {134}, number = {4}, year = {2006}, doi = {10.24033/bsmf.2522}, mrnumber = {2364944}, zbl = {1181.35355}, language = {en}, url = {http://www.numdam.org/articles/10.24033/bsmf.2522/} }
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 SP - 559 EP - 631 VL - 134 IS - 4 PB - Société mathématique de France UR - http://www.numdam.org/articles/10.24033/bsmf.2522/ DO - 10.24033/bsmf.2522 LA - en ID - BSMF_2006__134_4_559_0 ER -
%0 Journal Article %A Lerner, Nicolas %T Cutting the loss of derivatives for solvability under condition $(\Psi )$ %J Bulletin de la Société Mathématique de France %D 2006 %P 559-631 %V 134 %N 4 %I Société mathématique de France %U http://www.numdam.org/articles/10.24033/bsmf.2522/ %R 10.24033/bsmf.2522 %G en %F BSMF_2006__134_4_559_0
Lerner, Nicolas. Cutting the loss of derivatives for solvability under condition $(\Psi )$. Bulletin de la Société Mathématique de France, Volume 134 (2006) no. 4, pp. 559-631. doi : 10.24033/bsmf.2522. http://www.numdam.org/articles/10.24033/bsmf.2522/
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