Abstract
In this paper, we investigate the lack of compactness of the Sobolev embedding of $H^1(\mathbb R^2)$ into the Orlicz space $L^{{\phi}_p}(\mathbb R^2)$ associated to the function $\phi_p$ defined by $ \phi_p(s):={\rm{e}^{s^2}}-\sum_{k=0}^{p-1} \frac{s^{2k}}{k!}$. We also undertake the study of a nonlinear wave equation with exponential growth where the Orlicz norm $\|.\|_{L^{\phi_p}}$ plays a crucial role. This study includes issues of global existence, scattering and qualitative study.
Citation
Ines Ben Ayed. Mohamed Khalil Zghal. "Description of the lack of compactness in Orlicz spaces and applications." Differential Integral Equations 28 (5/6) 553 - 580, May/June 2015. https://doi.org/10.57262/die/1427744101
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