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2014 H1Lp versus C1 Local Minimizers
Yansheng Zhong
Abstr. Appl. Anal. 2014: 1-6 (2014). DOI: 10.1155/2014/646145


We show that a local minimizer of Φ in the C1 topology must be a local minimizer in the H1Lp topology, under suitable assumptions for the functional Φ=(1/2)|u|2+(1/p)|u|pF(x,u) with supercritical exponent p>2=2n/(n2). This result can be used to establish a solution to the corresponding equation admitting sub- and supersolution. Hence, we extend the conclusion proved by Brezis and Nirenberg (1993), the subcritical and critical case.


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Yansheng Zhong. "H1Lp versus C1 Local Minimizers." Abstr. Appl. Anal. 2014 1 - 6, 2014.


Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07022818
MathSciNet: MR3206811
Digital Object Identifier: 10.1155/2014/646145

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
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