非正则区域上的加权分数阶Sobolev-Poincaré不等式  

Weighted Fractional Sobolev-PoincaréInequalities in Irregular Domains

作　　者：宣一 Yi XUAN(Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China;School of Mathematical Sciences,University of Chinese Academy of Science,Beijing 100049,P.R.China)

机构地区：[1]中科院数学与系统科学研究院,北京100190 [2]中国科学院大学数学科学学院,北京100049

出　　处：《数学学报（中文版）》2024年第3期428-443,共16页Acta Mathematica Sinica：Chinese Series

摘　　要：本文研究了非正则区域的加权分数阶Sobolev-Poincaré不等式.这里考虑的权重是到边界距离的某次幂,并且这些区域是所谓的-John区域和β-Hölder区域.我们的主要结果将Hajlasz-Koskela的文[J.Lond.Math.Soc.,1998,58(2):425-450]结果从经典加权Sobolev-Poincaré不等式推广到它的分数阶对应式,并且将Guo的文[Chin.Ann.Math.,2017,38B(3):839-856]从分数阶Sobolev-Poincaré不等式推广到其加权情形.We study weighted fractional Sobolev-Poincaréinequalities in irregular domains.The weights considered here are distances to the boundary to certain powers,and the domains are the so-called-John domains and β-Hölder domains.Our main results extend that of Hajlasz-Koskela[J.Lond.Math.Soc.,1998,58(2):425-450]from the classical weighted Sobolev-Poincaréinequality to its fractional counter-part and Guo[Chin.Ann.Math.,2017,38B(3):839-856]from the fractional Sobolev-Poincaréinequality to its weighted case.

关 键 词：s-John区域 β-Hölder区域 分数阶Sobolev-Poincaré不等式 容量估计 权 

分 类 号：O178[理学—数学]