A non-linear problem involving a critical Sobolev exponent

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:396

Article

Bae, Soohyun²  Hadiji, Rejeb¹  Vigneron, Francois¹  Yazidi, Habib^1,3 

[1] Univ Paris Est, Lab Anal & Math Appl, UMR 8050, CNRS, F-94010 Creteil, France

[2] Hanbat Natl Univ, Taejon 305719, South Korea

[3] ESSTT Dept Math, Tunis 1008, Tunisia

关键词: Critical Sobolev exponent;    Minimization problem;    Non-linear effects;   

DOI  :  10.1016/j.jmaa.2012.06.001

来源: Elsevier

【 摘 要 】

We study a non-linear minimization problem on H-0(1)(Omega) subset of L-q with q = 2n/n-2: inf(parallel to u parallel to Lq=1) . integral Omega(1 + vertical bar x vertical bar(beta)vertical bar u vertical bar(k))vertical bar del u vertical bar(2). We show that minimizers exist only for the range beta < kn/q which corresponds to a dominant non-linear term. However, for beta >= kn/q the influence of linearity prevents their existence. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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