𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Coefficients with unbounded derivatives in hyperbolic equations

✍ Scribed by Massimo Cicognani

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
212 KB
Volume
276
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We are concerned with the problem of determining the sharp regularity of the coefficients with respect to the time variable t in order to have a well‐posed Cauchy problem in H^∞^ or in Gevrey classes for linear or quasilinear hyperbolic operators of higher order. We use and mix two different scales of regularity of global and local type: the modulus of HΓΆlder continuity and/or the behaviour with respect to |t βˆ’ t~1~|^βˆ’q^, q β‰₯ 1, of the first derivative as t tends to a point t~1~. Both are ways to weaken the Lipschitz regularity. (Β© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

πŸ“œ SIMILAR VOLUMES

Elliptic Equations with Discontinuous Co
Elliptic Equations with Discontinuous Coefficients in Weighted Sobolev Spaces on Unbounded Domains
✍ Patrizia Di Gironimo; Antonio Vitolo πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 105 KB

In this paper we study an elliptic linear operator in weighted Sobolev spaces and show existence and uniqueness theorems for the Dirichlet problem when the coefficients are given in suitable spaces of Morrey type, improving the previous results known in the literature.