Anisotropic versions of the Brezis-Van Schaftingen-Yung approach at s = 1 and s = 0

نویسندگان

چکیده

In 2014, Ludwig showed the limiting behavior of anisotropic Gagliardo s-seminorm a function f as s→1− and s→0+, which extend results due to Bourgain-Brezis-Mironescu (BBM) Maz'ya-Shaposhnikova (MS) respectively. Recently, Brezis, Van Schaftingen Yung provided different approach by replacing strong Lp norm in weak quasinorm. They characterized case for s=1 that complements BBM formula. The corresponding MS formula s=0 was later established first author. this paper, we follow Brezis-Van Schaftingen-Yung show versions s=0. Our result generalizes work Schaftingen, author Ludwig.

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ژورنال

عنوان ژورنال: Journal of Mathematical Analysis and Applications

سال: 2023

ISSN: ['0022-247X', '1096-0813']

DOI: https://doi.org/10.1016/j.jmaa.2023.127156