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 $f(x)=e^{g(|x|)}$ for $x \in \mathbb{R}^n}$, with $g$ smooth, convex and even. Then we give some of its applications to variational inequalities and PDEs via weighted symmetrization.
Barbara Brandolini, Francesco Chiacchio (2023). Some applications of the Chambers isoperimetric inequality. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S, 16(6), 1242-1263 [10.3934/dcdss.2022163].
Some applications of the Chambers isoperimetric inequality
Barbara Brandolini
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2023-06-01
Abstract
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 $f(x)=e^{g(|x|)}$ for $x \in \mathbb{R}^n}$, 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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