Singular perturbation for the first eigenfunction and blow-up analysis

Forum Mathematicum

Volumn 18, Issue 3, 2006, Pages 445-518

  Holcman, David ^a   Kupka, Ivan ^b  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^b SORBONNE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 23844549975     PISSN: 09337741     EISSN: 09337741     Source Type: Journal    
DOI: 10.1515/FORUM.2006.025     Document Type: Article

References (34)

1. Aubin T.: Some Nonlinear Problems in Riemannian Geometry. Springer, 1998
2. Devinatz A., Ellis R., Friedman A.: The Asymptotic Behavior of the First Real Eigenvalue of Second Order Elliptic Operators with a Small Parameter in the Highest Derivative, II. Indiana Univ. Math. J. 23 (1974), 991-1011
3. Devinatz A., Friedman A.: Asymptotic Behavior of the Principal Eigenfunction for a Singularly Perturbed Dirichlet Problem. Indiana Univ. Math. J. 27 (1978), 143-157
4. Devinatz A., Friedman A.: The Asymptotic behavior of the solution of a singular perturbed Dirichlet problem. Indiana Univ. Math. J. 27 (1978), 527-537
5. 2Δu - v(x)u. Theor. and Math. Phys. 87 (1991), 561-599
6. Donsker M., Varadhan S.: On a variational formula for the principal eigenvalue for the operators with maximum principle. Proc. Nat. Acad. Sci. USA 72 (1975), 780-783
7. Fleming W.: Controlled Markov Processes. 1986, Pisa
8. Freidlin M., Wentzell A.: Random Perturbations of Dynamical Systems. Springer-Verlag, 1984
9. Friedman A.: The Asymptotic Behavior of the First Real Eigenvalue of Second Order Elliptic Operators with a Small Parameter in the Highest Derivative. Indiana Univ. Math. J. 22 (1973), 1005-1015
10. Gilbarg D., Trudinger N.: Elliptic Partial Differentiable Equations of Second Order. Springer-Verlag 1983, second edition
11. Helffer B., Sjöstrand J.: Multiple Wells in the semi-classical limit I. Comm. in P.D.E 9 (1984), 337-408
12. Helffer B.: Semiclassical analysis for the Schrödinger operator and applications. Springer Lectures Notes in Math. 1336, 1988
13. Holcman D., Kupka I.: Singular Perturbation and first order PDE on manifolds. C. R. Acad. Sci. Paris Sér. I Math. 333 (2001), 465-470
14. Holcman D., Kupka I.: Semi-classical limit of the first eigenfunction and concentration on the recurent sets of a dynamical system, pre-print
15. Holcman D., Marchevska A., Schuss Z.: The survival probability of diffusion with killing, pre-print
16. Holland C.: Stochastically perturbated limit cycles. J. Appl. Prob. 15 (1978), 311-320
17. Kamin S.: Exponential descent of solutions of elliptic singular perturbation problems. Comm P.D.E 9 (1984), 197-213
18. Kamin S.: Singular perturbation problems and Hamilton-Jacobi. Integral Equations and Operator Theory 9 (1986), 95-105
19. Kifer Y.: Stochastic stability of the topological pressure. J. Analyse Math. 38 (1980), 255-286
20. Kifer Y.: On the principal eigenvalue in a singular perturbation problem with hyperbolic limit points and circles. J. Differential Equations 37 (1980), 108-139
21. Kifer Y.: Random Perturbations of Dynamical Systems. Birkäuser, 1988
22. Kifer Y.: Principal eigenvalues, topological pressure, and stochastic stability of equilibrium states. Israel J. Math. 70 (1990), 1-47
23. Krasnoselskii M.: Positive Solutions of Operator Equations. Noordhoff, Groningen 1967
24. Krylov N.: Lectures on Elliptic and Parabolic Equations in Hölder Spaces. Graduate Studies in Mathematics 12
25. Pinsky R.: Positive harmonic functions and diffusion. Cambridge Studies in Advanced Mathematics 45. Cambridge University Press, Cambridge 1995
26. Robinson C.: Dynamical Systems. CRC press 1995
27. Reed M., Simon B.: Methods of Modern Mathematical Physics. Academic Press, 1987
28. Rogers L., Williams D.: Diffusions, Markov Processes and Martingales. Wiley, 1987
29. Schuss Z.: Theory and Applications of Stochastic Differential Equations. Wiley Series in Probability and Statistics. John Wiley Sons, Inc., New York 1980
30. Simon B.: Semiclassical analysis of low lying eigenvalues I. Non-degenerate Minima: Asymptotic expansion. Ann. Inst. Henri Poincaré Vol. XXXVIII, 3 (1983), 295-307
31. Simon B.: Semiclassical analysis of low lying eigenvalues. II tunneling. Ann. of Math. 120 (1984), 89-118
32. Simon B.: Semi-classical analysis of low lying eigenvalues, IV. The flea on the elephant. J. Funct. Anal. 63 (1985), 123-136
33. Smale S.: Differential Dynamical Systems. Bull. Amer. Math. Soc. (1967), 747-830
34. Stroock D.: An Introduction to the Theory of Large Deviations. Springer, 1984