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A nonlinear inequality of Moser-Trudinger type

✍ Scribed by Gang Tian; Xiaohua Zhu

Publisher
Springer
Year
2000
Tongue
English
Weight
76 KB
Volume
10
Category
Article
ISSN
0944-2669

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Let (Σ , g) be a compact Riemannian surface without boundary. In this paper we shall use blowing up analysis to prove that sup Furthermore we show that there exists an extremal function for the above inequality. In other words, we show that sup Σ |∇u| 2 f dV g =1, Σ udV g =0 Σ e 4π f u 2 dV g is at