A note on complete hyperbolic operators with log-Zygmund coefficients

Ferruccio Colombini (1) , Francesco Fanelli (2) , Daniele del Santo (3) , Guy Metivier (4)

1 Dipartimento di Matematica
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
3 Università degli studi di Trieste = University of Trieste
4 IMB - Institut de Mathématiques de Bordeaux

The present paper is the continuation of the recent work [7], and it is devoted to strictly hyperbolic operators with non-regular coefficients. We focus here on the case of complete operators whose second order coefficients are log-Zygmund continuous in time, and we investigate the H∞ well-posedness of the associate Cauchy problem.

Domaines: Equations aux dérivées partielles [math.AP]

Ferruccio Colombini, Francesco Fanelli, Daniele del Santo, Guy Metivier. A note on complete hyperbolic operators with log-Zygmund coefficients. Fourier Analysis. Pseudo-differential operators, time-frequency analysis and partial differential equations. Edited by Michael Ruzhansky and Ville Turunen., Birkhäuser/Springer, 2014, Trends in Mathematics. ⟨hal-00795817⟩