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

2018/05/04 by Alvino, Angelo, Brock, Friedemann, Chiacchio, Francesco +2 · 1 citation
#35P15 #46E30 #46E35 #51M16 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1805.02518

Abstract

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 |x|^k x_N^α. Our results imply some sharp functional inequalities, like for instance, Caffarelli-Kohn-Nirenberg type inequalities.

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• Quantitative isoperimetric inequalities in capillarity problems and cones in strong and barycentric forms

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