Lipschitz continuity of the scattering operator for nonlinear Klein-Gordon equations

Artikel i vetenskaplig tidskrift, 2011

Abstract. We will give an overview of the Strichartz and Space Time Integral estimates for the Klein-Gordon and subcritical nonlinear Klein-Gordon equations, respectively. In this frame- work, the regularity of the solution and scattering operators for the nonlinear subcritical Klein- Gordon is studied, mainly using these tools and estimates of the nonlinearity in Besov spaces. We prove that these operators are (uniformly) Hölder continuous on the energy space for space dimension n >= 3, and Lipschitz continuous for n <= 8. AMS Subject Classification: 35L71, 35L10, 46E35.