On the solvability of pseudodifferential operators

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Abstract

We give a new proof of the Nirenberg-Treves conjecture: that local solvability of principal type pseudodifferential 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 3/2 derivatives (compared with the elliptic case), using some ideas of Nicolas Lerner.

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Forskningsområden

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Matematik

Nyckelord

Originalspråkengelska
Titel på värdpublikationSeminaire: Equations aux Dérivées Partielles. 2005--2006
FörlagÉcole Polytechnique, Centre de Mathématiques, Palaiseau, France
Antal sidor29
Volym1
ISBN (tryckt)2-7302-1335-X
StatusPublished - 2006
PublikationskategoriForskning
Peer review utfördJa
EvenemangSeminaire: Equations aux Dérivées Partielles - École Polytechnique, Centre de Mathématiques, Palaiseau, Frankrike
Varaktighet: 0001 jan 2 → …

Publikationsserier

Namn
Volym1

Konferens

KonferensSeminaire: Equations aux Dérivées Partielles
LandFrankrike
OrtÉcole Polytechnique, Centre de Mathématiques, Palaiseau
Period0001/01/02 → …