Rendiconti del Seminario Matematico della Università di Padova


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Volume 133, 2015, pp. 197–214
DOI: 10.4171/RSMUP/133-10

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

Michele Marini[1] and Berardo Ruffini[2]

(1) Dipartimento di Matematica, Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126, Pisa, Italy
(2) Institut Fourier, UMR 5582, Université Grenoble I, 100 rue des Maths, B.P. 74, 38402, Saint-Martin-d’Hères CEDEX, France

We solve a class of weighted isoperimetric problems of the form $$ \mathrm {min}\left\{\int_{\partial E}w e^V\,dx:\int_E e^V\,dx=\mathrm {constant}\right\}$$ where $w$ and $V$ are suitable functions on $\mathbb R^d$. As a consequence, we prove a comparison result for the solutions of degenerate elliptic equations.

Keywords: Weighted isoperimetric inequalities, symmetrizations, rearrangements

Marini Michele, Ruffini Berardo: On a class of weighted Gauss-type isoperimetric inequalities and applications to symmetrization. Rend. Sem. Mat. Univ. Padova 133 (2015), 197-214. doi: 10.4171/RSMUP/133-10