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Singular perturbation problems and the Hamilton-Jacobi equation

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References

  1. M. G. Crandall and P. L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 277 (1983), 1–42.

    Google Scholar 

  2. M. G. Crandall, L. C. Evans and P. L. Lions, Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 282 (1984), 487–502.

    Google Scholar 

  3. L. C. Evans and H. Ishii, A PDE approach to some asymptotic problems concerning random differential equations with small noise intensities, to appear.

  4. W. H. Fleming, Exit Probabilities and Optimal Stochastic Control, Appl. Math. Optim. 4 (1978), 329–346.

    Google Scholar 

  5. F. R. Gantmakher, The theory of matricex, Chelsea Publ., N. Y., 1959.

    Google Scholar 

  6. S. Kamenomostskaya, The first boundary value problem for elliptic equations containing a small parameter, Izv. Akad. Nauk USSR, ser. mat. 19 (1955), 345–360 (Russian).

    Google Scholar 

  7. S. Kamin, On singular perturbation problems with several turning points. Ind. Univ. Math. J. 31 (1982), 819–841.

    Google Scholar 

  8. S. Kamin, Exponential descent of solutions of elliptic singular perturbation problems. Comm. PDE (1984), 9 (2) 197–213.

    Google Scholar 

  9. S. N. Kružkov, Generalized solutions of the Hamilton-Jacobi equations of eikonal type. I. Formulation of the problems; existence, uniqueness and stability theorems; some properties of the solutions, Math. U.S.S.R. Sbornik, 27 (1975), 406–446.

    Google Scholar 

  10. N. Levinson, The first boundary value problem for εΔu+A(x,y)ux+B(x,y)uy+C(x,y)u=D(x,y) for small ε, Ann. of Math. 51 (1950), 428–445.

    Google Scholar 

  11. P. L. Lions, Generalized solutions of Hamilton-Jacobi equations, Pitman, London, 1982.

    Google Scholar 

  12. B. J. Matkowsky and Z. Schuss, The exit problem for randomly perturbed dynamical systems, SIAM J. Appl. Math. 33 (1977), 365–382.

    Google Scholar 

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dedicated to the memory of David Milman

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Kamin, S. Singular perturbation problems and the Hamilton-Jacobi equation. Integr equ oper theory 9, 95–105 (1986). https://doi.org/10.1007/BF01257063

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