H1∩Lp versus C1 Local Minimizers

Yansheng Zhong

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: We show that a local minimizer of Φ in the C1 topology must be a local minimizer in the H1∩Lp topology, under suitable assumptions for the functional Φ=(12/)∫Ω|∇u|2+(1/p)∫Ω|u|p−∫ΩF(x,u) with supercritical exponent p > 2∗ = 2n/(n − 2). 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.

Date: 2014
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https://doi.org/10.1155/2014/646145

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:646145

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