Best constants and minimizers for embeddings of second order Sobolev spaces

被引：8
|
作者：
Berchio, Elvise
Gazzola, Filippo
机构：
[1] Univ Turin, Dipartimento Matemat, I-10123 Turin, Italy
[2] Politecn Milan, Dipartimento Matemat, I-20133 Milan, Italy
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2006年 / 320卷 / 02期
关键词：
Sobolev embeddings; biharmonic operator; complementing condition;
D O I：
10.1016/j.jmaa.2005.07.052
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
By considering the kernels of the first two traces, four different second order Sobolev spaces may be constructed. For these spaces, embeddings into Lebesgue spaces, the best embedding constant and the possible existence of minimizers are studied. The Euler equation corresponding to some of these minimization problems is a semilinear biharmonic equation with boundary conditions involving third order derivatives: it is shown that the complementing condition is satisfied. (C) 2005 Elsevier Inc. All rights reserved.
引用
收藏
页码：718 / 735
页数：18
相关论文
共 50 条
  • [1] On Best Constants for Limiting Embeddings of Fractional Sobolev Spaces
    Costa, David G.
    de Figueiredo, Djairo G.
    Yang, Jianfu
    [J]. ADVANCED NONLINEAR STUDIES, 2010, 10 (02) : 501 - 510
  • [2] Best constants for two families of higher order critical Sobolev embeddings
    Shafrir, Itai
    Speetor, Daniel
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2018, 177 : 753 - 769
  • [3] Bounds for best constants in subcritical Sobolev embeddings
    Cassani, Daniele
    Tarsi, Cristina
    Zhang, Jianjun
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2019, 187 : 438 - 449
  • [4] EMBEDDINGS OF SOBOLEV SPACES OF FRACTIONAL ORDER
    MARTINS, JS
    [J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1977, 79 : 1 - 24
  • [5] On a problem of Huang concerning best constants in Sobolev embeddings
    Giovanni Anello
    Francesca Faraci
    Antonio Iannizzotto
    [J]. Annali di Matematica Pura ed Applicata (1923 -), 2015, 194 : 767 - 779
  • [6] On a problem of Huang concerning best constants in Sobolev embeddings
    Anello, Giovanni
    Faraci, Francesca
    Iannizzotto, Antonio
    [J]. ANNALI DI MATEMATICA PURA ED APPLICATA, 2015, 194 (03) : 767 - 779
  • [7] Best constants in second-order Sobolev inequalities on Riemannian manifolds and applications
    Biezuner, RJ
    Montenegro, M
    [J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2003, 82 (04): : 457 - 502
  • [8] BEST CONSTANTS IN INEQUALITIES INVOLVING SOBOLEV SPACES
    CHERRIER, P
    [J]. BULLETIN DES SCIENCES MATHEMATIQUES, 1984, 108 (03): : 225 - 262
  • [9] Characterizations of second order Sobolev spaces
    Cui, Xiaoyue
    Lam, Nguyen
    Lu, Guozhen
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2015, 121 : 241 - 261
  • [10] Positivity, symmetry and uniqueness for minimizers of second-order Sobolev inequalities
    Alberto Ferrero
    Filippo Gazzola
    Tobias Weth
    [J]. Annali di Matematica Pura ed Applicata, 2007, 186 : 565 - 578
12345