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We study the isoperimetric problem in endowed with a mixed Euclidean–Log-convex measure . We prove the existence of an isoperimetric set and we show some of its qualitative properties.
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Nicola Fusco, Diego Pallara, On the isoperimetric profile for a mixed Euclidean–Log-convex measure. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 28 (2017), no. 4, pp. 635–661