On the <i>L</i> <sub> <i>q</i> </sub>-reflector problem in ℝ<sup> <i>n</i> </sup> with non-Euclidean norm
نویسندگان
چکیده
Abstract In this article, we introduce a class of geometric optics measure-the L q Σ {L}_{q}\hspace{0.33em}\Sigma -reflector measure which arises from an {L}_{q} extension the \Sigma measure. And ask Minkowski-type problem for measure, called problem. It is shown that foundations such have been laid by Caffarelli et al. ( Reflector in endowed with non-Euclidean norm , Arch. Ration. Mech. Anal. 193 (2009), no. 2, 445–473) (for measure). Inspired Alexandrov, present some variational arguments and existence results solutions to
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ژورنال
عنوان ژورنال: Advanced Nonlinear Studies
سال: 2022
ISSN: ['1536-1365', '2169-0375']
DOI: https://doi.org/10.1515/ans-2022-0009