The purpose of this note is to present an anisotropic variant of the BMO-type norm introduced in [4] and to show its relation with a surface measure, which is indeed a multiple of the perimeter in the isotropic case. This is done in the spirit of the new characterization of the perimeter of a measurable set in Rn recently studied by Ambrosio, Bourgain, Brezis and Figalli in [2].
Calculus of variations — BMO-type norms and anisotropic surface measures, by Giovanni E. Comi, communicated on February 9, 2018
Comi, Giovanni E.
2018
Abstract
The purpose of this note is to present an anisotropic variant of the BMO-type norm introduced in [4] and to show its relation with a surface measure, which is indeed a multiple of the perimeter in the isotropic case. This is done in the spirit of the new characterization of the perimeter of a measurable set in Rn recently studied by Ambrosio, Bourgain, Brezis and Figalli in [2].File in questo prodotto:
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BMO-type_norms_anistropic_surface_measures.pdf
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