Gagliardo-Nirenberg inequalities involving the gradient L2-norm

被引:27
作者
Agueh, Martial [1 ]
机构
[1] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3P4, Canada
基金
加拿大自然科学与工程研究理事会;
关键词
D O I
10.1016/j.crma.2008.05.015
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We present a method giving the sharp constants and optimal functions of all the Gagliardo-Nirenberg inequalities involving the L-2-norm of the gradient. We show that the optimal functions can be explicitly derived from a specific non-linear ordinary differential equation which appears to be linear for a subclass of the Gagliardo-Nirenberg inequalities or when the space dimension reduces to 1. In these cases, we give the explicit expressions of the optimal functions, along with the sharo constants of the corresponding Gagliardo-Nirenberg inequalities. Our method extend to the L-p-Gagliardo-Nirenberg and L-p-Nash's inequalities for all p > 1.
引用
收藏
页码:757 / 762
页数:6
相关论文
共 10 条
  • [1] Sharp Gagliardo-Nirenberg inequalities and mass transport theory
    Agueh, M.
    [J]. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2006, 18 (04) : 1069 - 1093
  • [2] Geometric inequalities via a general comparison principle for interacting gases
    Agueh, M
    Ghoussoub, N
    Kang, X
    [J]. GEOMETRIC AND FUNCTIONAL ANALYSIS, 2004, 14 (01) : 215 - 244
  • [3] AGUEH M, NONLINEAR DIFF UNPUB
  • [4] Carlen E., 1993, Int. Math. Res. Not., V1993, P213, DOI DOI 10.1155/S1073792893000224
  • [5] A mass-transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities
    Cordero-Erausquin, D
    Nazaret, B
    Villani, C
    [J]. ADVANCES IN MATHEMATICS, 2004, 182 (02) : 307 - 332
  • [6] Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions
    Del Pino, M
    Dolbeault, J
    [J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2002, 81 (09): : 847 - 875
  • [7] Gagliardo E., 1958, RIC MAT, V7, P102
  • [8] Levine H. A., 1980, ANN MAT PUR APPL, V4, P181, DOI [10.1007/BF01795392, DOI 10.1007/BF01795392]
  • [9] Nirenberg L., 1959, ANN SCUOL NORM SUP P, V13, P116
  • [10] Serrin J, 2000, INDIANA U MATH J, V49, P897