Applied Mathematics and Optimization

, Volume 23, Issue 1, pp 1–15

Remarks on elliptic singular perturbation problems

Authors

  • Hitoshi Ishii
    • Department of MathematicsChuo University
  • Shigeaki Koike
    • Department of MathematicsTokyo Metropolitan University
Article

DOI: 10.1007/BF01442390

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

Abstract

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