Some applications of the chambers isoperimetric inequality

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S（2023）

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摘要

In this paper, using the Chambers isoperimetric inequality, we introduce the notion of weighted rearrangement of a function associated to the measure f dx, where f(x) = eg(|x|) for x & ISIN; Rn, with g smooth, convex and even. Then we give some of its applications to variational inequalities and PDEs via weighted symmetrization.

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关键词

Weighted isoperimetric inequalities,rearrangements,symmetrization,sharp estimates,eigenvalues

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