On the Solvability of Systems of Pseudodifferential Operators
Author
Summary, in English
We study the solvability for a system of pseudodifferential operators. We will assume that the systems is of principal type, i.e., the principal symbol vanishes of first order on the kernel, and that the eigenvalue close to zero has constant multiplicity. We prove that local solvability is to condition (PSI) on the eigenvalues as in the scalar case. This condition rules out any sign changes from
- to + of the imaginary part of the eigenvalue when going in the positive direction on the 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). But we need no conditions on the lower order terms.
- to + of the imaginary part of the eigenvalue when going in the positive direction on the 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). But we need no conditions on the lower order terms.
Department/s
- Mathematics (Faculty of Sciences)
- Partial differential equations
Publishing year
2008
Language
English
Publication/Series
Rapport TVBM / Avdelningen för byggnadsmaterial, Tekniska högskolan i Lund
Links
Document type
Other
Topic
- Mathematics
Keywords
- principal type
- systems of pseudodifferential operators
- constant characteristics
- solvability
Status
Unpublished
Research group
- Partial differential equations
ISBN/ISSN/Other
- ISSN: 0348-7911
- arXiv:0801.4043