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
✦ LIBER ✦
A Trudinger-Moser inequality in a weighted Sobolev space and applications
✍ Scribed by Furtado, Marcelo F.; Medeiros, Everaldo S.; Severo, Uberlandio B.
- Book ID
- 121694856
- Publisher
- John Wiley and Sons
- Year
- 2014
- Tongue
- English
- Weight
- 294 KB
- Volume
- 287
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
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## Abstract This paper deals with an improvement of a class of the Trudinger‐Moser inequality with a singular weight associated to the embedding of the standard Sobolev space __H__^1^~0~(Ω) into Orlicz spaces for any smooth domain \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyl
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