Year: 2001
Journal of Partial Differential Equations, Vol. 14 (2001), Iss. 2 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2001-JPDE-5478
Journal of Partial Differential Equations, Vol. 14 (2001), Iss. 2 : pp. 163–192
Published online: 2001-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
Keywords: Moser-Trüdinger inequality