The proof of the Nirenberg-Treves conjecture

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Abstract

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).

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Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Matematik

Nyckelord

Originalspråkengelska
Titel på värdpublikationJournées "Équations aux Dérivées Partielles"
FörlagUniv. Nantes, Nantes, France
Antal sidor25
ISBN (tryckt)2-86939-207-9
StatusPublished - 2003
PublikationskategoriForskning
Peer review utfördJa
EvenemangJournées "Équations aux Dérivées Partielles" - Forges-les-Eaux, Frankrike
Varaktighet: 2003 jun 2 → …

Konferens

KonferensJournées "Équations aux Dérivées Partielles"
LandFrankrike
OrtForges-les-Eaux
Period2003/06/02 → …