# DESCRIPTION OF THE LACK OF COMPACTNESS IN ORLICZ SPACES AND APPLICATIONS

1 LAMA - Laboratoire d-Analyse et de Mathématiques Appliquées

Abstract : 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 ϕp defined by $\phi ps:={ m{e}^{s^2}}-\Sum {k=0}^{p-1} \frac{s^{2k}}{k!}\cdot$ We also undertake the study of a nonlinear wave equation with exponential growth where the Orlicz norm ∥.∥Lϕp plays a crucial role. This study includes issues of global existence, scattering and qualitative study.

Author: Ines Ben Ayed - Mohamed Khalil Zghal -

Source: https://hal.archives-ouvertes.fr/