Asymptotics of Green functions and Martin boundaries for elliptic operators with periodic coefficients

详细信息    查看全文

• 作者：Murata ; Minoru ; Tsuchida ; Tetsuo
• 关键词：31C35 ; 35J99 ; 35B40 (primary) ; 35B10 ; 31B25 ; 31B35 (secondary) ; Green function ; Elliptic equation ; Periodic coefficients ; Martin boundary
• 刊名：Journal of Differential Equations
• 出版年：2003
• 出版时间：November 20, 2003
• 年：2003
• 卷：195
• 期：1
• 页码：82-118
• 全文大小：423 K

文摘

We give the asymptotics at infinity of a Green function for an elliptic equation with periodic coefficients on R^d. Basic ingredients in establishing the asymptotics are an integral representation of the Green function and the saddle point method. We also completely determine the Martin compactification of R^d with respect to an elliptic equation with periodic coefficients by using the exact asymptotics at infinity of the Green function.