On a class of weighted Gauss-type isoperimetric inequalities and applications to symmetrization

Michele Marini; Berardo Ruffini

doi:10.4171/rsmup/133-10

JournalsrsmupVol. 133pp. 197–214

On a class of weighted Gauss-type isoperimetric inequalities and applications to symmetrization

Michele Marini
Scuola Normale Superiore, Pisa, Italy
Berardo Ruffini
Université Grenoble I, Saint-Martin-d'Hères, France

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Abstract

We solve a class of weighted isoperimetric problems of the form

min {\int_{\partial E} w e^{V} d x : \int_{E} e^{V} d x = constant}

where $w$ and $V$ are suitable functions on $R^{d}$ . As a consequence, we prove a comparison result for the solutions of degenerate elliptic equations.

Cite this article

Michele Marini, Berardo Ruffini, On a class of weighted Gauss-type isoperimetric inequalities and applications to symmetrization. Rend. Sem. Mat. Univ. Padova 133 (2015), pp. 197–214

DOI 10.4171/RSMUP/133-10