Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


The Cauchy problem for a class of Kovalevskian pseudo-differential operators
HTML articles powered by AMS MathViewer

by Rossella Agliardi and Massimo Cicognani PDF
Proc. Amer. Math. Soc. 132 (2004), 841-845 Request permission


We prove the $H^{\infty }$ well-posedness of the forward Cauchy problem for a pseudo-differential operator $P$ of order $m\geq 2$ with the Log-Lipschitz continuous symbol in the time variable. The characteristic roots $\lambda _k$ of $P$ are distinct and satisfy the necessary Lax-Mizohata condition Im$\lambda _k\geq 0$. The Log-Lipschitz regularity has been tested as the optimal one for $H^{\infty }$ well-posedness in the case of second-order hyperbolic operators. Our main aim is to present a simple proof which needs only a little of the basic calculus of standard pseudo-differential operators.
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35G10, 35L30
  • Retrieve articles in all journals with MSC (2000): 35G10, 35L30
Additional Information
  • Rossella Agliardi
  • Affiliation: University of Ferrara, via Machiavelli 35, 44100 Ferrara, Italy
  • Email:
  • Massimo Cicognani
  • Affiliation: University of Bologna, via Genova 181, 47023 Cesena, Italy
  • Email:
  • Received by editor(s): September 30, 2002
  • Received by editor(s) in revised form: November 5, 2002
  • Published electronically: August 19, 2003
  • Communicated by: David S. Tartakoff
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 841-845
  • MSC (2000): Primary 35G10, 35L30
  • DOI:
  • MathSciNet review: 2019963