Some inequalities of Glaeser-Bronšteĭn type
Sergio Spagnolo
Università di Pisa, ItalyGiovanni Taglialatela
Università degli Studi di Bari, Italy
Abstract
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
Sergio Spagnolo, Giovanni Taglialatela, 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