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On the Sharp Gårding Inequality for Operators with Polynomially Bounded and Gevrey Regular Symbols

Author

Listed:
  • Alexandre Arias Junior

    (Department of Mathematics, Federal University of Paraná, Curitiba 81531-980, Brazil)

  • Marco Cappiello

    (Department of Mathematics, University of Turin, Via Carlo Alberto 10, 10123 Turin, Italy)

Abstract

In this paper, we analyze the Friedrichs part of an operator with polynomially bounded symbol. Namely, we derive a precise expression of its asymptotic expansion. In the case of symbols satisfying Gevrey estimates, we also estimate precisely the regularity of the terms in the asymptotic expansion. These results allow new and refined applications of the sharp Gårding inequality in the study of the Cauchy problem for p -evolution equations.

Suggested Citation

  • Alexandre Arias Junior & Marco Cappiello, 2020. "On the Sharp Gårding Inequality for Operators with Polynomially Bounded and Gevrey Regular Symbols," Mathematics, MDPI, vol. 8(11), pages 1-23, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1938-:d:439198
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