Anisotropic Moser–Trudinger-Type Inequality with Logarithmic Weight

Tao Zhang () and Jie Liu
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Tao Zhang: School of Mathematics and Information Science, Yantai University, Yantai 264005, China
Jie Liu: School of Mathematics and Information Science, Yantai University, Yantai 264005, China

Mathematics, 2024, vol. 12, issue 5, 1-15

Abstract: Our main purpose in this paper is to study the anisotropic Moser–Trudinger-type inequalities with logarithmic weight ω β ( x ) = [ − ln F o ( x ) | ( n − 1 ) β . This can be seen as a generation result of the isotropic Moser–Trudinger inequality with logarithmic weight. Furthermore, we obtain the existence of extremal function when β is small. Finally, we give Lions’ concentration-compactness principle, which is the improvement of the anisotropic Moser–Trudinger-type inequality.

Keywords: anisotropic Moser–Trudinger-type inequality; logarithmic weight; existence of extremal function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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