![Sample our Mathematics & Statistics journals, sign in here to start your FREE access for 14 days]({"type":"image" , "src" : "/sda/5943/TOC-Subject-Sample-2021-Mathematics-Statistics.jpg"})
ABSTRACT
In this paper, we consider the asymptotic behavior for the principal eigenvalue of an elliptic operator with piecewise constant coefficients. This problem was first studied by Friedman in 1980. We show how the geometric shape of the interface affects the asymptotic behavior for the principal eigenvalue. This is a refinement of the result by Friedman.
Acknowledgements
The author would like to thank Professor Shigeru Sakaguchi (Tohoku University) for many stimulating discussions. Also the author would like to thank Lorenzo Cavallina (Tohoku University) for his warm encouragement.
Disclosure statement
No potential conflict of interest was reported by the author.
Additional information
Funding
This research was partially supported by the Grant-in-Aid for Scientific Research (B) [#26287020] and Challenging Exploratory Research [#16K13768] of Japan Society for the Promotion of Science.