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Asymptotics of Green functions and Martin boundaries for elliptic operators with periodic coefficients |
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| Authors: | Minoru Murata |
| Affiliation: | a Department of Mathematics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan b Department of Mathematics, Meijo University, Shiogamaguchi, Tenpaku-ku, Nagoya 468-8502, Japan |
| Abstract: | We give the asymptotics at infinity of a Green function for an elliptic equation with periodic coefficients on Rd. 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 Rd with respect to an elliptic equation with periodic coefficients by using the exact asymptotics at infinity of the Green function. |
| Keywords: | 31C35 35J99 35B40 (primary) 35B10 31B25 31B35 (secondary) |
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