A quasi-linear elliptic equation with critical growth on compact Riemannian manifold without boundary

作者：do O, Joao Marcos; Yang, Yunyan^*

来源：Annals of Global Analysis and Geometry, 2010, 38(3): 317-334.

DOI：10.1007/s10455-010-9218-0

• Trudinger-Moser inequality
• Adams inequality
• Critical growth
• N-Laplacian

Let (M, g) be an N-dimensional compact Riemannian manifold without boundary. When m is a positive integer strictly smaller than N, we prove that, and alpha (N,m) is the best constant in Adams' original inequality (Ann Math 128:385-398, 1988). This is a modified version of Adams' inequality on compact Riemannian manifold which has been proved by Fontana (Comment Math Helv 68:415-454, 1993). Using the above inequality in the case when m = 1, we establish sufficient conditions under which the quasi-linear equation for some gamma > 0.

• 出版日期2010-10
• 单位中国人民大学