Abstract
We give a 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 two derivatives (compared with the elliptic case).
| Original language | English |
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| Title of host publication | Graduate Series in Analysis |
| Editors | Ferruccio Colombini, Tatsuo Nishitani |
| Publisher | International Press, Somerville, MA, USA |
| Pages | 159-184 |
| Number of pages | 26 |
| ISBN (Print) | 1-57146-150-7 |
| Publication status | Published - 2003 |
| Event | Hyperbolic problems and related topics - Cortona, Italy Duration: 2002 Sept 10 → … |
Conference
| Conference | Hyperbolic problems and related topics |
|---|---|
| Country/Territory | Italy |
| City | Cortona |
| Period | 2002/09/10 → … |
Subject classification (UKÄ)
- Mathematics
Free keywords
- pseudodifferential operators
- Nirenberg-Treves conjecture
- solvability
- principal type