@Article{JPDE-14-163, author = {Yuxiang Li }, title = {Moser-Trudinger Inequality on Compact Riemannian Manifolds of Dimension Two}, journal = {Journal of Partial Differential Equations}, year = {2001}, volume = {14}, number = {2}, pages = {163--192}, abstract = { ln this paper, we prove Moser-Trüdinger inequality in any two dimensional manifolds. Let (M,g_M,) be a two dimensional manifold without boundary and (g, g_N) with boundary, we shall prove the following three inequalities: u∈H¹(M), \sup\limits_{and ||u||_{H¹(M)}}=1∫_M^{e^{4\pi u²}<+∞} u∈H¹(M), \sup\limits_{∫_M u=0, and} ∫_M|∇u|²=1∫_M^{e^{4\pi u²}<+∞} u∈H¹_0(N), \sup\limits_{and ∫_M|∇u²|=1∫_M^{e^{4\pi u²}<+∞} Moreover, we shall show that there exist of extremal functions which at tain the above three inequalities.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5478.html} }