### $L^p$-$L^q$ estimates for regularly linear hyperbolic systems

#### Abstract

In this paper we establish $L^p-L^q$ estimates for the solution of the strictly hyperbolic first-order linear systems with bounded time-dependent coefficients. In the equation setting, Reissig and others obtained such estimates by using WKB representations of the solutions. Here the crucial point is to find minimal assumptions on the coefficients of the system so that Reissig's approach still works for systems.

#### Article information

Source
Adv. Differential Equations Volume 14, Number 9/10 (2009), 801-834.

Dates
First available in Project Euclid: 18 December 2012

Mathematical Reviews number (MathSciNet)
MR2548279

Zentralblatt MATH identifier
1183.35066

#### Citation

D'Abbicco, Marcello; Lucente, Sandra; Taglialatela, Giovanni. $L^p$-$L^q$ estimates for regularly linear hyperbolic systems. Adv. Differential Equations 14 (2009), no. 9/10, 801--834. https://projecteuclid.org/euclid.ade/1355863331

#### Corrections

• Correction: Marcello Dâ€™Abbico, Sandra Lucente, Giovanni Taglialatela. Errata to "$L^p$--$L^q$ estimates for regularly linear hyperbolic systems". Adv. Differential Equations 16 (2011), no. 1-2, 199â€“200.