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.
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Communicated by W. Fleming
H. Ishii was supported in part by the AFOSR under Grant No. AFOSR 85-0315 and the Division of Applied Mathematics, Brown University.
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Ishii, H., Koike, S. Remarks on elliptic singular perturbation problems. Appl Math Optim 23, 1–15 (1991). https://doi.org/10.1007/BF01442390
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DOI: https://doi.org/10.1007/BF01442390