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arXiv · 1805.02518

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

Angelo Alvino·Friedemann Brock·Francesco Chiacchio·Anna Mercaldo·Maria Rosaria Posteraro
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Abstract

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.

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Angelo Alvino, Friedemann Brock, Francesco Chiacchio, Anna Mercaldo, Maria Rosaria Posteraro. 2018-05-04. The isoperimetric problem for a class of non-radial weights and applications. https://arxiv.org/abs/1805.02518

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