title: The Pólya-Szegö principle and the anisotropic convex Lorentz-Sobolev inequality.
abstract: An anisotropic convex Lorentz-Sobolev inequality is established, which extends Ludwig, Xiao, and Zhang's result to any norm from Euclidean norm, and the geometric analogue of this inequality is given. In addition, it implies that the (anisotropic) Pólya-Szegö principle is shown.
authors.affiliation: Department of Mathematics, Shanghai University, Shanghai 200444, China.
authors.forename: Shuai
authors.initials: S
authors.lastname: Liu
authors.affiliation: Department of Mathematics, Shanghai University, Shanghai 200444, China.
authors.forename: Binwu
authors.initials: B
authors.lastname: He
mesh_terms: D016880:Anisotropy; D008962:Models, Theoretical