Minimal rearrangements of Sobolev functions: A new proof.
The authors give a new and elegant proof of Pólya-Szegő type inequalities for functions \(u\in W^{1,p}_0(\Omega)\) and their Schwarz-symmetrizations or radially symmetric rearrangements \(u^*\). They discuss in particular the case of equality in such inequalities and give an alternative proof of the well-known result of Brother and Ziemer.
scientific article; zbMATH DE number 1912454
scientific article