Moser-Trudinger Inequality on Compact Riemannian Manifolds of Dimension Two

Moser-Trudinger Inequality on Compact Riemannian Manifolds of Dimension Two

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