Advances in Differential Equations
- Adv. Differential Equations
- Volume 14, Number 9/10 (2009), 801-834.
$L^p$-$L^q$ estimates for regularly linear hyperbolic systems
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.
Adv. Differential Equations, Volume 14, Number 9/10 (2009), 801-834.
First available in Project Euclid: 18 December 2012
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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
- Correction: Marcello DâAbbico, Sandra Lucente, Giovanni Taglialatela. Errata to "$L^p$--$L^q$ estimates for regularly linear hyperbolic systems". Adv. Differential Equations 16 (2011), no. 1-2, 199â200.