An isoperimetric inequality for Gauss-like product measures

作者：Brock F; Chiacchio F^*; Mercaldo A

来源：Journal de Mathematiques Pures et Appliquees, 2016, 106(2): 375-391.

DOI：10.1016/j.matpur.2016.02.014

• Relative isoperimetric inequalities
• Polya-Szego principle
• Degenerate elliptic equations

This paper deals with various questions related to the isoperimetric problem for a smooth positive measure d mu = phi(x)d(x), with x epsilon Omega subset of R-N. Firstly we find some necessary conditions on the density of the measure phi(x) that render the intersection of half spaces with Omega a minimum in the isoperimetric problem. We then identify the unique isoperimetric set for a wide class of factorized finite measures. These results are finally used in order to get sharp inequalities in weighted Sobolev spaces and a comparison result for solutions to boundary value problems for degenerate elliptic equations.

• 出版日期2016-8