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math.FA2025
Approximation of rearrangements by polarizations
Gabriele Bianchi, Richard J. Gardner, Paolo Gronchi +1
The symmetric decreasing rearrangement of functions on features in several seminal inequalities, such as the Pólya-Szegő inequality. The latter was shown by the auth…
math.FA2024★ 2 cited
Anisotropic symmetrization, convex bodies, and isoperimetric inequalities
Gabriele Bianchi, Andrea Cianchi, Paolo Gronchi
This work is concerned with a Pólya-Szegö type inequality for anisotropic functionals of Sobolev functions. The relevant inequality entails a double-symmetrization involving both t…
math.FA2022★ 5 cited
The Pólya-Szegő inequality for smoothing rearrangements
Gabriele Bianchi, Richard J. Gardner, Paolo Gronchi +1
A basic version of the Pólya-Szegő inequality states that if is a Young function, the -Dirichlet energy -- the integral of -- of a suitable function $f\in…