度量测度空间中障碍问题解的Caccioppoli型不等式

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

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.