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Existence and boundedness of a minimiser for a constrained minimisation problem on Rn with limiting exponent

Published online by Cambridge University Press:  14 November 2011

Shen Yaotian  and
Yan Shusen
Shen Yaotian
Affiliation:
Department of Applied Mathematics, South China University of Technology, Guangzhou 510641, P.R. China
Yan Shusen
Affiliation:
Department of Applied Mathematics, South China University of Technology, Guangzhou 510641, P.R. China
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Synopsis

We use the concentration compactness principle to study the existence of a minimiser of the minimisation problem where u =(u1, …, uN), . We also prove the boundedness of the minimiser of l1 by using the reverse Holder inequality.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 122 , Issue 3-4 , 1992 , pp. 221 - 235
Copyright
Copyright © Royal Society of Edinburgh 1992

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