publications

Article

Description of the lack of compactness in Orlicz spaces and applications,

Ben Ayed Ines, Zghal Mohamed Khalil, 2015

Differential and Integral Equations, 28, 5, 553-580, Février 2015

Résumé

In this paper, we investigate the lack of compactness of the Sobolev embedding of $H^1(\R^2)$ into the Orlicz space $L^{\phi_p}(\R^2)$ associated to the function $\phi_p(s):=e^{s^2}-\Sum_{k=0}^{p-1} \frac{s^{2k}{k!}$. We also unsertake the study of a nonlinear wave equation with an exponential growth where the Orlicz norm plays a crucial role. This study includes isuues of global existence, scattering and qualitative study.