Abstract
This paper is devoted to the description of the lack of compactness of H rad 1 ( R 2 ) in the Orlicz space. Our result is expressed in terms of the concentration-type examples derived by P.-L. Lions (1985) in [24]. The approach that we adopt to establish this characterization is completely different from the methods used in the study of the lack of compactness of Sobolev embedding in Lebesgue spaces and takes into account the variational aspect of Orlicz spaces. We also investigate the feature of the solutions of nonlinear wave equation with exponential growth, where the Orlicz norm plays a decisive role.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
