Geodesic
The resolution of the Nirenberg–Treves conjecture
Nils Dencker1
1 Centre for Mathematical Sciences, University of Lund, 221 00 Lund, Sweden
Annals of mathematics, Tome 163 (2006) no. 2, pp. 405-444.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We give a proof of the Nirenberg-Treves conjecture: that local solvability of principal-type pseudo-differential operators is equivalent to condition ($\Psi$). This condition rules out sign changes from $-$ to $+$ of the imaginary part of the principal symbol along the oriented bicharacteristics of the real part. We obtain local solvability by proving a localizable a priori estimate for the adjoint operator with a loss of two derivatives (compared with the elliptic case).
DOI : 10.4007/annals.2006.163.405

Nils Dencker 1

1 Centre for Mathematical Sciences, University of Lund, 221 00 Lund, Sweden 
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Nils Dencker. The resolution of the Nirenberg–Treves conjecture. Annals of mathematics, Tome 163 (2006) no. 2, pp. 405-444. doi : 10.4007/annals.2006.163.405. http://geodesic.mathdoc.fr/articles/10.4007/annals.2006.163.405/

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