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Anisotropic Moser–Trudinger-Type Inequality with Logarithmic Weight

Author

Listed:
  • 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)

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.

Suggested Citation

  • Tao Zhang & Jie Liu, 2024. "Anisotropic Moser–Trudinger-Type Inequality with Logarithmic Weight," Mathematics, MDPI, vol. 12(5), pages 1-15, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:785-:d:1352561
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