度量测度空间中障碍问题解的Caccioppoli 型不等式

(西北工业大学 理学院,西安 710129

度量测度空间; 障碍问题; Caccioppoli型不等式; 有界性

Caccioppoli Type Inequalities for Solutions to Obstacle Problems in Metric Measure Spaces
WANG Huiju

(School of Natural and Applied Sciences,Northwestern Polytechnical University,Xi'an 710129,China)

metric measure space; obstacle problem; Caccioppoli type inequality; boundedness

DOI: 10.16185/j.jxatu.edu.cn.2019.06.001 http://xb.xatu.edu.cn

备注

为了研究在度量情形下Orlicz-Sobolev空间中的障碍问题,本文通过选取适当的截断函数,利用 “填洞法” 证明了障碍问题解的Caccioppoli型不等式。文中结论为研究障碍问题解的有界性的提供了理论基础。

In order to study the obstacle problems in Orlicz-Sobolev spaces in the metric setting,suitable cutoff functions and the “hole-filing” method are applied to establish Caccioppoli type inequalities for solutions to obstacle problems.The result obtained offers a theoretical basis for the study of the boundedness of solutions to obstacle problems.