A sharp form of the Moser-Trudinger inequality on a compact Riemannian surface

By Y. Yang. 2007

98 citations recorded by the source corpus.

In this paper, a sharp form of the Moser-Trudinger inequality is established on a compact Riemannian surface via the method of blow-up analysis, and the existence of an extremal function for such an inequality is proved

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b06fee5c0767b4cb5ac7236c58a4693112c33b92

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In Applied Mathematics

1. Nguyen Huong Lam
2. G. Lu
3. Y. Yang
4. Xiaobao Zhu
5. Caifeng Zhang
6. Hanli Tang
7. Federica Sani
8. Jiuyi Zhu

In Computational Theory and Mathematics

1. G. Lu
2. Nguyen Huong Lam
3. Y. Yang
4. Xiaobao Zhu
5. Caifeng Zhang
6. Federica Sani
7. Hanli Tang
8. Jiuyi Zhu

In Mathematical Physics

1. G. Lu
2. Nguyen Huong Lam
3. Xiaobao Zhu
4. Y. Yang
5. Hanli Tang
6. Caifeng Zhang
7. Jiuyi Zhu

Citations in the corpus

• Blow-up analysis concerning singular Trudinger–Moser inequalities in dimension two (2016, background): “Yang [28, 29] to the cases of high dimension and compact Riemannian surface, by Lu-Yang [19] and J.”
• Extremal functions for Trudinger-Moser inequalities of Adimurthi-Druet type in dimension two (2015, background): “In [41], we proved the following: For anyα, 0≤ α < λ1(Σ), there holds sup u∈W1,2(Σ), ‖∇gu‖2≤1, ∫”
• Sharp constant and extremal function for the improvedMoser-Trudinger inequality involving $L^p$ norm in two dimension (2009, unknown): “9), as we did in [28, 29], we set β̃ = G+ 1 2π log r − Ax0 , where x0 is the concentration point as before, r(x) = |x− x0|, and whence β̃ = O(r).”
• Adams' inequalities for bi-Laplacian and extremal functions in dimension four (2009, unknown): “Then we have v 2 2 = =u 2 2 + t 2 u 0 2 2 + 2t Ω u u 0 dx = t 2 + 2t Ω u u 0 dx + O 1/ log 1 , G. Lu, Y. Yang / Advances in Mathematics 220 (2009) 1135–1170 v 2 2 = =u 2 2 + t 2 u 0 2 2 + 2t Ω u u 0 dx = 1 + 2λ(Ω)t Ω u u 0 dx + λ(Ω)t 2 + O 1/ log 1 .”
• EXISTENCE OF NONTRIVIAL SOLUTIONS TO POLYHARMONIC EQUATIONS WITH SUBCRITICAL AND CRITICAL EXPONENTIAL GROWTH (2012, background): “We also refer the reader to the survey article by S.Y. A. Chang and P. Yang on Moser-Trudinger inequalities and their applications in PDEs [10].”