A new technique to study the boundary behaviors of superharmonic multifunctions and their application

Boundary value problems

Yong Lu¹  Jianguo Sun² 

[1] College of Power and Energy Engineering, Harbin Engineering University, Harbin, China;Department of Computer Science and Technology, Harbin Engineering University, Harbin, China

关键词: superharmonic function;    superharmonic multifunction;    boundary behavior;   

DOI  :  10.1186/s13661-017-0874-x

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Using some recent results of the Riesz decomposition method for sharp estimates of certain boundary value problems of harmonic functions in (St. Cer. Mat. 27:323-328, 1975), the boundary behaviors of upper and lower superharmonic multifunctions are studied. Several fundamental properties of these new classes of these functions are shown. A new technique is proposed to find the exact boundary behaviors by using Levin’s type boundary behaviors for harmonic functions admitting certain lower bounds in (Pacific J. Math. 15:961-970, 1965). Finally, some examples are given to illustrate the applications of our results.

【 授权许可】

CC BY