On the Solvability of Systems of Pseudodifferential Operators

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Abstract

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.

Detaljer

Författare
Enheter & grupper
Forskningsområden

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Matematik

Nyckelord

Originalspråkengelska
Antal sidor38
StatusUnpublished - 2008
PublikationskategoriForskning

Publikationsserier

NamnRapport TVBM / Avdelningen för byggnadsmaterial, Tekniska högskolan i Lund
ISSN (tryckt)0348-7911