arXiv:1805.02518 Abstract | arXiv Analytics

arXiv:1805.02518 [math.AP]Abstract References Reviews Resources

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

Angelo Alvino, Friedemann Brock, Francesco Chiacchio, Anna Mercaldo, Maria Rosaria Posteraro

Published 2018-05-04Version 1

We study a class of isoperimetric problems on $\mathbb{R}^{N}_{+} $ where the densities of the weighted volume and weighted perimeter are given by two different non-radial functions of the type $|x|^k x_N^\alpha$. Our results imply some sharp functional inequalities, like for instance, Caffarelli-Kohn-Nirenberg type inequalities.

Comments: arXiv admin note: text overlap with arXiv:1606.02195

Categories: math.AP

Subjects: 51M16, 46E35, 46E30, 35P15

Keywords: isoperimetric problem, non-radial weights, applications, caffarelli-kohn-nirenberg type inequalities, sharp functional inequalities

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