Optimal improved L-p-Riemannian Gagliardo-Nirenberg inequalities

作者：Sun Xiaomei^*; Chen Wenyi

来源：Nonlinear Analysis-Theory Methods & Applications, 2010, 72(6): 3159-3172.

DOI：10.1016/j.na.2009.12.009

• Improved Gagliardo-Nirenberg inequality
• Best constant
• Validity

Let (M, g) be a compact Riemannian manifold of dimension n >= 3. This article is devoted to proving the validity of the optimal improved Cagliardo-Nirenberg type inequality for p > 2:
(integral(M)vertical bar u vertical bar(t)d upsilon(g))(2/r0) <= (A(p,q,r)(2/p) (integral(M)vertical bar del(g)u vertical bar(p)d nu(g))(2/p) + B(integral(M)vertical bar u vertical bar(p)d upsilon(g)) x (integral(M)vertical bar u vertical bar(q)d upsilon g)(2(1-0)/0q),
which supplements the results in Ceccon and Mentenegro (2008) [13].

• 出版日期2010-3-15
• 单位武汉大学