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Rendiconti Lincei - Matematica e Applicazioni


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Volume 28, Issue 4, 2017, pp. 635–661
DOI: 10.4171/RLM/780

Published online: 2017-11-15

On the isoperimetric profile for a mixed Euclidean–Log-convex measure

Nicola Fusco[1] and Diego Pallara[2]

(1) Università degli Studi di Napoli Federico II, Italy
(2) Università degli Studi di Lecce, Italy

We study the isoperimetric problem in $\mathbb R^h\times\mathbb R^k$ endowed with a mixed Euclidean–Log-convex measure $\lambda=e^{\psi(x)}\, dxdy$. We prove the existence of an isoperimetric set and we show some of its qualitative properties.

Keywords: Isoperimetric problem, mixed densities, existence and properties of minimizers

Fusco Nicola, Pallara Diego: On the isoperimetric profile for a mixed Euclidean–Log-convex measure. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 28 (2017), 635-661. doi: 10.4171/RLM/780