Sharp Adams-type inequality invoking Hardy inequalities

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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].

Keywords

Trudinger–Moser inequalities Hardy inequalities Orlicz space lack of compactness 

Mathematics Subject Classification

46E35 35B33 46E30 

Notes

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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Copyright information

© Indian Academy of Sciences 2018

Authors and Affiliations

  1. 1.Laboratoire Équations aux dérivées partielles (LR03ES04), Faculté des Sciences de TunisUniversité de Tunis El ManarTunisTunisia

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