Optimal partial regularity of very weak solutions to nonhomogeneous A-harmonic systems

Journal of inequalities and applications

Qing Zhao¹ 

关键词: nonhomogeneous A-harmonic systems;    very weak solution;    optimal partial regularity;    Hodge decomposition;    A-harmonic approximation technique;   

DOI  :  10.1186/s13660-017-1297-z

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We study partial regularity of very weak solutions to some nonhomogeneous A-harmonic systems. To obtain the reverse Hölder inequality of the gradient of a very weak solution, we construct a suitable test function by Hodge decomposition. With the aid of Gehring’s lemma, we prove that these very weak solutions are weak solutions. Further, we show that these solutions are in fact optimal Hölder continuity based on A-harmonic approximation technique.

【 授权许可】

CC BY