一类椭圆型方程弱解的正则性  

Regularity of the weak solutions for a class of elliptic equations

作　　者：狄华斐[1] 周道军[1] 郑治波[2] 

机构地区：[1]云南民族大学数学与计算机科学学院,云南昆明650500 [2]云南师范大学数学学院,云南昆明650092

出　　处：《重庆文理学院学报（自然科学版）》2011年第5期5-8,共4页Journal of Chongqing University of Arts and Sciences

摘　　要：在一定条件假设下,讨论了一类椭圆型方程Lu=finU初值问题的弱解的正则性.通过一些技巧和方法,描述了弱解的内部正则性.这些技巧和方法包括截断函数、边界的展平、有限覆盖定理、sobolev不等式、内插不等式等.In this paper,the regularity of the weak solution to the initial value problem for second-order elliptic equations Lu=f in U under some conditions assumptions was discussed.Through some techniques and methods,the interior regularity of the weak solution was described.These techniques and methods include cut off function,flatten out the boundary,finitely covered theorem,sobolev inequalities,interpolation inequalities,etc.

关 键 词：椭圆型方程 弱解 截断函数 内部正则性 

分 类 号：O175.25[理学—数学]