Harnack inequality and regularity of p-Laplace equation on complete manifolds

Kodai Mathematical Journal

Xi Zhang¹ 

[1] DEPARTMENT OF MATHEMATICS ZHEJIANG UNIVERSITY (XX)

关键词: Complete manifold;    p-Laplace Operator;    Poincaré inequality;    Hölder continuouty;    Moser's iteration;   

DOI  :  10.2996/kmj/1138044262

学科分类：数学（综合）

来源: Tokyo Institute of Technology, Department of Mathematics

【 摘 要 】

References(5)In this paper, we will derive a mean value inequality and a Harnack inequality for nonnegative functions which satisfies the differential inequality |div(|f|p−2∇f)|≤A   fp−1 in the weak sence on complete manifolds, where constants A≥0, p>1; as a consequence, we give a Cα estimate for weak solutions of the above differential inequality, then we generalize the results in [1], [2]. We would thank Professor Z. G. Bai and Professor Y. B. Shen for their long time encourgement, we also thank the referee for invaluable comments.

【 授权许可】

Unknown