Higher integrability for obstacle problem related to the singular porous medium equation

被引：0
作者：
Li, Qifan [1 ]
机构：
[1] Wuhan Univ Technol, Sch Sci, Dept Math, 122 Luoshi Rd, Wuhan 430070, Hubei, Peoples R China
来源：
BOUNDARY VALUE PROBLEMS | 2020年 / 2020卷 / 01期
关键词：
Obstacle problem; Porous medium equation; Quasilinear parabolic equation; Self-improving property; PARABOLIC-SYSTEMS; WEAK SOLUTIONS;
D O I：
10.1186/s13661-020-01445-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we study the self-improving property of the obstacle problem related to the singular porous medium equation by using the method developed by Gianazza and Schwarzacher (J. Funct. Anal. 277(12):1-57,2019). We establish a local higher integrability result for the spatial gradient of themth power of nonnegative weak solutions, under some suitable regularity assumptions on the obstacle function. In comparison to the work by Cho and Scheven (J. Math. Anal. Appl. 491(2):1-44,2020), our approach provides some new aspects in the estimations of the nonnegative weak solution of the obstacle problem.
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页数：36
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