The isoperimetric problem for a class of non-radial weights and applications

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:267

Article

Alvino, A.¹  Brock, F.²  Chiacchio, F.¹  Mercaldo, A.¹  Posteraro, Mr¹ 

[1] Univ Napoli Federico II, Dipartimento Matemat & Applicaz R Caccioppoli, Complesso Monte S Angelo,Via Cintia, I-80126 Naples, Italy

[2] Swansea Univ, Coll Sci, Dept Math, Bay Campus,Fabian Way, Swansea SA1 8EN, W Glam, Wales

关键词: Isoperimetric inequality;    Weighted rearrangement;    Functional inequalities;   

DOI  :  10.1016/j.jde.2019.07.013

来源: Elsevier

【 摘 要 】

We study a class of isoperimetric problems on R-+(N) where the densities of the weighted volume and weighted perimeter are given by two different non-radial functions of the type vertical bar x vertical bar(k) x(N)(alpha) . Our results imply some sharp functional inequalities, like for instance, Caffarelli-Kohn-Nirenberg type inequalities. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free