Some inequalities of Glaeser-Bronšteĭn type

  • Giovanni Taglialatela

    Università degli Studi di Bari, Italy
  • Sergio Spagnolo

    Università di Pisa, Italy


The classical Glaeser estimate is a special case of the Lemma of Bronšteĭn which states the Lipschitz continuity of the roots of a hyperbolic polynomial with coefficients depending on a real parameter. Here we prove a pointwise estimate for the successive derivatives of the 's in term of certain nonnegative functions which are symmetric polynomials of the roots (hence also of the coefficients . These inequalities are very helpful in the study of the Cauchy problem for homogeneous weakly hyperbolic equations of higher order.

Cite this article

Giovanni Taglialatela, Sergio Spagnolo, Some inequalities of Glaeser-Bronšteĭn type. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 17 (2006), no. 4, pp. 367–375

DOI 10.4171/RLM/474