The differentiability of solutions for elliptic equations which degenerate on part of the boundary of a convex domain  

作　　者：SONG Jia-xin CAO Yi 

机构地区：[1]Department of Mathematics and Information Science, Shaanxi Normal University

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2018年第4期421-435,共15页高校应用数学学报（英文版）（B辑）

基　　金：Research supported by the National Natural Science Foundation of China(11671243);the Shaanxi natural science basic research project of China(2018JM1020)

摘　　要：In this paper,we study the differentiability of solutions on the boundary for equartions of type L;u=;u/x;+|x|;;u/y;=f（x,y）,where λ is an arbitrary positive number. By introducing a proper metric that is related to the elliptic operator L;, we prove the differentiability on the boundary when some well-posed boundary conditions are satisfied. The main difficulty is the construction of new barrier functions in this article.In this paper,we study the differentiability of solutions on the boundary for equartions of type L_λu=~2u/x^2+|x|^(2λ)~2u/y^2=f(x,y),where λ is an arbitrary positive number. By introducing a proper metric that is related to the elliptic operator L_λ, we prove the differentiability on the boundary when some well-posed boundary conditions are satisfied. The main difficulty is the construction of new barrier functions in this article.

关 键 词：elliptic equations convex domain DIFFERENTIABILITY 

分 类 号：O1[理学—数学]