STUDY OF FRACTIONAL POINCARE INEQUALITIES ON UNBOUNDED DOMAINS

被引：12

作者：

Chowdhury, Indranil ^{[1
]}

Csato, Gyula ^{[2
]}

Roy, Prosenjit ^{[3
]}

Firoj, S. K. ^{[3
]}

机构：

[1] Norwegian Univ Sci & Technol, Dept Math Sci, NO-7491 Trondheim, Norway

[2] Univ Barcelona, Barcelona, Spain

[3] Indian Inst Technol, Dept Math & Stat, Kanpur 208016, Uttar Pradesh, India

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2021年 / 41卷 / 06期

关键词：

Fractional Poincare inequality; fractional-Sobolev spaces; unbounded domains; infinite strips like domains; (regional) fractional Laplacian; BREZIS-NIRENBERG RESULT; ASYMPTOTIC-BEHAVIOR; EQUATIONS; SET; SPACES;

D O I：

10.3934/dcds.2020394

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this paper is to study (regional) fractional Poincare type inequalities on unbounded domains satisfying the finite ball condition. Both existence and non existence type results on regional fractional inequality are established depending on various conditions on domains and on the range of s is an element of (0, 1). The best constant in both regional fractional and fractional Poincare inequality is characterized for strip like domains (omega -> Rn-1), and the results obtained in this direction are analogous to those of the local case. This settles one of the natural questions raised by K. Yeressian in [Asymptotic behavior of elliptic nonlocal equations set in cylinders, Asymptot. Anal. 89, (2014), no 1-2].

引用

页码：2993 / 3020

页数：28

共 50 条

[31] L(φ, μ)-averaging domains and Poincare inequalities with Orlicz norms
Ding, Shusen
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 73 (01) : 256 - 265
[32] Equivalence of analytic and Sobolev Poincare inequalities for planar domains
Stanoyevitch, A
Stegenga, DA
PACIFIC JOURNAL OF MATHEMATICS, 1997, 178 (02) : 363 - 375
[33] Fractional Poincare and logarithmic Sobolev inequalities for measure spaces
Gressman, Philip T.
JOURNAL OF FUNCTIONAL ANALYSIS, 2013, 265 (06) : 867 - 889
[34] Fractional Poincare and localized Hardy inequalities on metric spaces
Dyda, Bartlomiej
Lehrback, Juha
Vahakangas, Antti V.
ADVANCES IN CALCULUS OF VARIATIONS, 2023, 16 (04) : 867 - 884
[35] POINCAR INEQUALITIES ON UNBOUNDED DOMAINS AND STRONG NONLINEAR VARIATIONS
沈尧天
顾永耕
A Monthly Journal of Science, 1982, (10) : 1033 - 1036
[36] Eigenvalue inequalities for Schrodinger operators on unbounded Lipschitz domains
Behrndt, Jussi
Rohleder, Jonathan
Stadler, Simon
JOURNAL OF SPECTRAL THEORY, 2018, 8 (02) : 493 - 508
[37] MAXIMUM PRINCIPLE IN UNBOUNDED DOMAINS FOR PARABOLIC INEQUALITIES WITH FUNCTIONALS
REDHEFFER, R
WALTER, W
MATHEMATISCHE ANNALEN, 1977, 226 (02) : 155 - 170
[38] Weak Poincare inequalities on domains defined by brownian rough paths
Aida, S
ANNALS OF PROBABILITY, 2004, 32 (04): : 3116 - 3137
[39] Unified Poincare and Hardy inequalities with sharp constants for convex domains
Avkhadiev, Farit G.
Wirths, Karl-Joachim
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 2007, 87 (8-9): : 632 - 642
[40] Poincare Inequalities with Luxemburg Norms in Lφ(m)-Averaging Domains
Xing, Yuming
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2010,

← 1 2 3 4 5 →