Ding, Weiyue; Jost, Jürgen; Li, Jiayu; Wang, Guofang The differential equation \(\Delta u=8\pi-8\pi he^u\) on a compact Riemann surface. (English) Zbl 0955.58010 Asian J. Math. 1, No. 2, 230-248 (1997). Summary: Let \(M\) be a compact Riemann surface, \(h(x)\) a positive smooth function on \(M\). We consider the functional \[ J(u)= \textstyle {1\over 2}\int_M|\nabla u|^2 +8\pi\int_M u-8\pi\log \int_M he^u. \] We give a sufficient condition under which \(J\) achieves its minimum. Cited in 3 ReviewsCited in 71 Documents MSC: 58E15 Variational problems concerning extremal problems in several variables; Yang-Mills functionals 35J60 Nonlinear elliptic equations 58J60 Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) Keywords:Nirenberg problem; compact Riemann surface PDF BibTeX XML Cite \textit{W. Ding} et al., Asian J. Math. 1, No. 2, 230--248 (1997; Zbl 0955.58010) Full Text: DOI