Weighted Sobolev spaces of radially symmetric functions

被引：27
|
作者：
Musina, Roberta [1 ]
机构：
[1] Univ Udine, Dipartimento Matemat & Informat, I-33100 Udine, Italy
来源：
ANNALI DI MATEMATICA PURA ED APPLICATA | 2014年 / 193卷 / 06期
关键词：
Rellich inequality; Sobolev inequality; Caffarelli-Kohn-Nirenberg inequality; Weighted biharmonic operator; Dilation invariance; SHARP CONSTANTS; INEQUALITIES; EXISTENCE;
D O I：
10.1007/s10231-013-0348-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove dilation invariant inequalities involving radial functions, poliharmonic operators and weights that are powers of the distance from the origin. Then, we discuss the existence of extremals, and in some cases, we compute the best constants.
引用
收藏
页码：1629 / 1659
页数：31
相关论文
共 50 条
  • [21] Embeddings of weighted Sobolev spaces and a weighted fourth-order elliptic equation
    Guo, Zongming
    Wan, Fangshu
    Wang, Liping
    COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2020, 22 (06)
  • [22] Sharp Sobolev and Adams-Trudinger-Moser embeddings on weighted Sobolev spaces and their applications
    do O, Joao Marcos
    Lu, Guozhen
    Ponciano, Raoni
    FORUM MATHEMATICUM, 2024, 36 (05) : 1279 - 1320
  • [23] Continuity of Embeddings of Weighted Sobolev Spaces in Lebesgue Spaces on Anisotropically Irregular Domains
    Trushin, B. V.
    PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2010, 269 (01) : 265 - 283
  • [24] On some bilinear problems on weighted Hardy-Sobolev spaces
    Cascante, C.
    Ortega, J. M.
    MATHEMATISCHE NACHRICHTEN, 2012, 285 (13) : 1616 - 1634
  • [25] Special embeddings of weighted Sobolev spaces with nontrivial power weights
    Rabier, Patrick J.
    COLLECTANEA MATHEMATICA, 2013, 64 (03) : 409 - 426
  • [26] Embedding theorems for weighted Sobolev spaces in a borderline case and applications
    Carvalho, J. L.
    Furtado, M. F.
    Medeiros, E. S.
    ANNALI DI MATEMATICA PURA ED APPLICATA, 2024, 203 (01) : 345 - 359
  • [27] COMPACT EMBEDDINGS ON A SUBSPACE OF WEIGHTED VARIABLE EXPONENT SOBOLEV SPACES
    Unal, Cihan
    Aydin, Ismail
    ADVANCES IN OPERATOR THEORY, 2019, 4 (02) : 388 - 405
  • [28] On a class of nonlinear degenerate elliptic equations in weighted Sobolev spaces
    El Ouaarabi, Mohamed
    Allalou, Chakir
    Melliani, Said
    GEORGIAN MATHEMATICAL JOURNAL, 2023, 30 (01) : 81 - 94
  • [29] Raviart-Thomas interpolation in fractional weighted Sobolev spaces
    Alvarez, Maria Luz
    Armentano, Maria Gabriela
    Duran, Ricardo G.
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2024, 168 : 39 - 45
  • [30] Weighted Sobolev spaces: Markov-type inequalities and duality
    Marcellan, Francisco
    Quintana, Yamilet
    Rodriguez, Jose M.
    BULLETIN OF MATHEMATICAL SCIENCES, 2018, 8 (02) : 233 - 256
12345