Applied Mathematics and Optimization

, Volume 23, Issue 1, pp 1–15

Remarks on elliptic singular perturbation problems

  • Hitoshi Ishii
  • Shigeaki Koike

DOI: 10.1007/BF01442390

Cite this article as:
Ishii, H. & Koike, S. Appl Math Optim (1991) 23: 1. doi:10.1007/BF01442390


We show the effectiveness of viscosity-solution methods in asymptotic problems for second-order 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.

Copyright information

© Springer-Verlag New York Inc. 1991

Authors and Affiliations

  • Hitoshi Ishii
    • 1
  • Shigeaki Koike
    • 2
  1. 1.Department of MathematicsChuo UniversityTokyoJapan
  2. 2.Department of MathematicsTokyo Metropolitan UniversityTokyoJapan

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