IMPROVED POINCARE INEQUALITIES IN FRACTIONAL SOBOLEV SPACES

被引：15
作者：
Drelichman, Irene [1 ]
Duran, Ricardo G. [1 ,2 ]
机构：
[1] Univ Buenos Aires, Fac Ciencias Exactas & Nat, IMAS, CONICET, RA-1428 Buenos Aires, DF, Argentina
[2] Univ Buenos Aires, Fac Ciencias Exactas & Nat, Dept Matemat, RA-1428 Buenos Aires, DF, Argentina
来源：
ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA | 2018年 / 43卷
关键词：
Sobolev inequality; Poincare inequality; fractional norms; weighted Sobolev spaces; John domains; s-John domains; cusp domains; WEIGHTED POINCARE;
D O I：
10.5186/aasfm.2018.4352
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We obtain improved fractional Poincare and Sobolev-Poincare inequalities including powers of the distance to the boundary in bounded John, s-John, and Holder-alpha domains, and discuss their optimality.
引用
收藏
页码：885 / 903
页数：19
相关论文
共 26 条
  • [11] On comparability of integral forms
    Dyda, B
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 318 (02) : 564 - 577
  • [12] On improved fractional Sobolev-Poincar, inequalities
    Dyda, Bartlomiej
    Ihnatsyeva, Lizaveta
    Vahakangas, Antti V.
    [J]. ARKIV FOR MATEMATIK, 2016, 54 (02): : 437 - 454
  • [13] Isoperimetric inequalities and imbedding theorems in irregular domains
    Hajlasz, P
    Koskela, P
    [J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1998, 58 : 425 - 450
  • [14] Pointwise estimates to the modified Riesz potential
    Harjulehto, Petteri
    Hurri-Syrjanen, Ritva
    [J]. MANUSCRIPTA MATHEMATICA, 2018, 156 (3-4) : 521 - 543
  • [15] An Embedding into an Orlicz space for L11-Functions from Irregular Domains
    Harjulehto, Petteri
    Hurri-Syrjaenen, Ritva
    [J]. COMPLEX ANALYSIS AND DYNAMICAL SYSTEMS VI, PT 1: PDE, DIFFERENTIAL GEOMETRY, RADON TRANSFORM, 2015, 653 : 177 - +
  • [16] CERTAIN CONVOLUTION INEQUALITIES
    HEDBERG, LI
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 36 (02) : 505 - 510
  • [17] A weighted Poincare inequality with a doubling weight
    Hurri-Syrjanen, R
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 126 (02) : 545 - 552
  • [18] On fractional Poincar, inequalities
    Hurri-Syrjanen, Ritva
    Vahakangas, Antti V.
    [J]. JOURNAL D ANALYSE MATHEMATIQUE, 2013, 120 : 85 - 104
  • [19] AN IMPROVED POINCARE INEQUALITY
    HURRISYRJANEN, R
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1994, 120 (01) : 213 - 222
  • [20] JOST J., 2002, GRAD TEXTS MATH, V214
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