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On a version of Trudinger–Moser inequality with Möbius shift invariance

✍ Scribed by Adimurthi; Kyril Tintarev


Publisher
Springer
Year
2010
Tongue
English
Weight
190 KB
Volume
39
Category
Article
ISSN
0944-2669

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A weighted form of Moser–Trudinger inequ
✍ Yunyan Yang 📂 Article 📅 2006 🏛 Elsevier Science 🌐 English ⚖ 219 KB

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