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May/June 2015 Description of the lack of compactness in Orlicz spaces and applications
Ines Ben Ayed, Mohamed Khalil Zghal
Differential Integral Equations 28(5/6): 553-580 (May/June 2015).

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

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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.

Information

Published: May/June 2015
First available in Project Euclid: 30 March 2015

zbMATH: 1363.46024
MathSciNet: MR3328134

Subjects:
Primary: 35B33 , 46E30 , 46E35

Rights: Copyright © 2015 Khayyam Publishing, Inc.

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Vol.28 • No. 5/6 • May/June 2015
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