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

We solve a class of weighted isoperimetric problems of the form

min{EweVdx:EeVdx=constant}\mathrm {min}\left\{\int_{\partial E}w e^V\,dx:\int_E e^V\,dx=\mathrm {constant}\right\}

where ww and VV are suitable functions on Rd\mathbb 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