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Modern Trends in Pseudo-Differential Operators

Volume 172 of the series Operator Theory: Advances and Applications pp 135-151

Gevrey Local Solvability for Degenerate Parabolic Operators of Higher Order

  • Alessandro OliaroAffiliated withDepartment of Mathematics, University of Torino
  • , Petar PopivanovAffiliated withInstitute of Mathematics and Informatics, Bulgarian Academy of Sciences

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Abstract

In this paper we study the local solvability in Gevrey classes for degenerate parabolic operators of order ≥ 2. We assume that the lower order term vanishes at a suitably smaller rate with respect to the principal part; we then analyze its influence on the behavior of the operator, proving local solvability in Gevrey spaces G s for small s, and local nonsolvability in G s for large s.

Keywords

Degenerate parabolic operators Gevrey classes local solvability non local solvability