一类椭圆型方程极大值原理的初步研究  

PRELIMINARY RESEARCH ON MAXIMUM PRINCIPLIES FOR A CLASS OF ELLIPTIC EQUATIONS

作　　者：张海亮[1] 金霁[1] 

机构地区：[1]山西大学经济系,河北工学院

出　　处：《山西大学学报（自然科学版）》1995年第2期123-127,共5页Journal of Shanxi University(Natural Science Edition)

摘　　要：关于椭圆型方程△ｕ＋ｆ（ｘ，ｕ）＝０解的“Ｐ－泛函”的极值原理是多年来遗留下的一个难题。本文利用Ｈｏｐｆ极值原理对此作了一些大胆探索，构造了该方程解的某合适泛函，获得了这类泛函的极大值原理。利用这些原理可获得解、解的梯度等重要物理量的界。For years it has remained a difficult problem to deduce maximum primciples for″P-functional″of elliptic equation △u+f(x,u)=0. The paper vigorously explores the problemsby the Hopf maximum principles,builds certain suitalbe functionals for the solutions of equa-tions, and obtains the maximum principles of the functionals.The principies derived may beused to deduce bounds of important quantities in some physics problems,such as,the solu-tions of equations and gradient of the solutions and so on.

关 键 词：椭圆型方程 极大值原理 

分 类 号：O175.25[理学—数学]