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Linearised Moser-Trudinger inequality

Published online by Cambridge University Press:  17 April 2009

Meelae Kim
Meelae Kim
Affiliation:
Center for Teaching and Research, Korea Polytechnic University, Jungwang-dong 3–101, Sihung-si, Kyunggi-do, Korea e-mail: [email protected]
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Abstract

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As a limiting case of the Sobolev imbedding theorem, the Moser-Trudinger inequality was obtained for functions in with resulting exponential class integrability. Here we prove this inequality again and at the same time get sharper information for the bound. We also generalise the Linearised Moser inequality to higher dimensions, which was first introduced by Beckner for functions on the unit disc. Both of our results are obtained by using the method of Carleson and Chang. The last section introduces an analogue of each inequality for the Laplacian instead of the gradient under some restricted conditions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 62 , Issue 3 , December 2000 , pp. 445 - 457
Copyright
Copyright © Australian Mathematical Society 2000

References

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