Some applications of the Chambers isoperimetric inequality

Abstract

<p style='text-indent:20px;'>In this paper, using the Chambers isoperimetric inequality, we introduce the notion of weighted rearrangement of a function associated to the measure <inline-formula><tex-math id="M1">\begin{document}$ f\,dx $\end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id="M2">\begin{document}$ f (x) = e^{g(|x|)} $\end{document}</tex-math></inline-formula> for <inline-formula><tex-math id="M3">\begin{document}$ x \in \mathbb{R}^n $\end{document}</tex-math></inline-formula>, with <inline-formula><tex-math id="M4">\begin{document}$ g $\end{document}</tex-math></inline-formula> smooth, convex and even. Then we give some of its applications to variational inequalities and PDEs via weighted symmetrization.</p>