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The affine Orlicz Pólya–Szegö principle on \(BV(\Omega )\)

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Abstract

The affine Orlicz Pólya–Szegö principles with respect to Steiner symmetrization and Schwarz symmetrization proved in Lin and Xing (International mathematics research notices, 2019) are extended to \(BV(\Omega )\), the space of functions of bounded variation defined in an open set \(\Omega \subset \mathbb {R}^n\), and their equality cases are characterized.

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Acknowledgements

I am very grateful to the referee for many valuable suggestions and comments.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, People’s Republic of China

    Youjiang Lin

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  1. Youjiang Lin
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Correspondence to Youjiang Lin.

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Communicated by N. Trudinger.

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Research of the author is supported by NSFC No. 11971080 and the funds of the Basic and Advanced Research Project of CQ CSTC cstc2015jcyjA00009, cstc2018jcyjAX0790 and Scientific and Technological Research Program of Chongqing Municipal Education Commission (KJ1500628).

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Lin, Y. The affine Orlicz Pólya–Szegö principle on \(BV(\Omega )\). Calc. Var. 58, 178 (2019). https://doi.org/10.1007/s00526-019-1622-0

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