Some isoperimetric inequalities on $\mathbb{R} ^N$ with respect to weights $|x|^\alpha

We solve a class of isoperimetric problems on $\mathbb{R}^N $ with respect to weights that are powers of the distance to the origin. For instance we show that if $k\in [0,1]$, then among all smooth sets $\Omega$ in $\mathbb{R} ^N$ with fixed Lebesgue measure, $\int_{\partial \Omega } |x|^k \, \maths...

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Bibliographische Detailangaben

Hauptverfasser:	Alvino, A, Brock, F, Chiacchio, F, Mercaldo, A, Posteraro, M. R
Format:	Artikel
Sprache:	eng
Schlagworte:	Mathematics - Functional Analysis
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