Abstract
We establish a sharp Trudinger–Moser type inequality invoking a Hardy inequality for any even dimension. This leads to a non compact Sobolev embedding in some Orlicz space. We also give a description of the lack of compactness of this embedding in the spirit of [8].
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Acknowledgements
The author is very grateful to Prof. Hajer Bahouri and Prof. Mohamed Majdoub for interesting discussions and careful reading of the manuscript. A part of this work was done at LAMA-Université Paris-Est Créteil whose hospitality and support is gratefully acknowledged.
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Zghal, M.K. Sharp Adams-type inequality invoking Hardy inequalities. Proc Math Sci 128, 13 (2018). https://doi.org/10.1007/s12044-018-0379-2
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DOI: https://doi.org/10.1007/s12044-018-0379-2