Advances in Differential Equations

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

Marcello D'Abbicco, Sandra Lucente, and Giovanni Taglialatela

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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

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

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35B45: A priori estimates 35L45: Initial value problems for first-order hyperbolic systems


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.

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  • Correction: Marcello D’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, 199–200.