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Remarks on elliptic singular perturbation problems
 Hitoshi Ishii,
 Shigeaki Koike
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We show the effectiveness of viscositysolution methods in asymptotic problems for secondorder elliptic partial differential equations (PDEs) with a small parameter. Our stress here is on the point that the methods, based on stability results [3], [16], apply without hard PDE calculations. We treat two examples from [11] and [23]. Moreover, we generalize the results to those for Hamilton—Jacobi—Bellman equations with a small parameter.
H. Ishii was supported in part by the AFOSR under Grant No. AFOSR 850315 and the Division of Applied Mathematics, Brown University.
Communicated by W. Fleming
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 Title
 Remarks on elliptic singular perturbation problems
 Journal

Applied Mathematics and Optimization
Volume 23, Issue 1 , pp 115
 Cover Date
 19910101
 DOI
 10.1007/BF01442390
 Print ISSN
 00954616
 Online ISSN
 14320606
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Authors

 Hitoshi Ishii ^{(1)}
 Shigeaki Koike ^{(2)}
 Author Affiliations

 1. Department of Mathematics, Chuo University, Bunkyoku, 112, Tokyo, Japan
 2. Department of Mathematics, Tokyo Metropolitan University, Setagayaku, 158, Tokyo, Japan