An asymptotic formula for the Green's function of an elliptic operator

Martino Bardi

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1987)

  • Volume: 14, Issue: 4, page 569-586
  • ISSN: 0391-173X

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Bardi, Martino. "An asymptotic formula for the Green's function of an elliptic operator." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 14.4 (1987): 569-586. <http://eudml.org/doc/84018>.

@article{Bardi1987,
author = {Bardi, Martino},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {smooth boundary; Dirac measure; Dirichlet problem; uniformly elliptic; rate of decay; representation formula},
language = {eng},
number = {4},
pages = {569-586},
publisher = {Scuola normale superiore},
title = {An asymptotic formula for the Green's function of an elliptic operator},
url = {http://eudml.org/doc/84018},
volume = {14},
year = {1987},
}

TY - JOUR
AU - Bardi, Martino
TI - An asymptotic formula for the Green's function of an elliptic operator
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1987
PB - Scuola normale superiore
VL - 14
IS - 4
SP - 569
EP - 586
LA - eng
KW - smooth boundary; Dirac measure; Dirichlet problem; uniformly elliptic; rate of decay; representation formula
UR - http://eudml.org/doc/84018
ER -

References

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  1. [1] M.G. Crandall, L.C. Evans, P.L. Lions, Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc.282 (1984), pp. 487-502. Zbl0543.35011MR732102
  2. [2] M.G. Crandall, P.L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc.277 (1983), pp. 1-42. Zbl0599.35024MR690039
  3. [3] M. Day, Exponential leveling for stochastically perturbed dynamical systems, SIAM J. Math. Anal.13 (1982), pp. 532-540. Zbl0513.60077MR661588
  4. [4] L.C. Evans, H. Ishii, A PDE approach to some asymptotic problems concerning random differential equations with small noise intensities, Ann. Inst. H. Poincaré Anal. Non Linéaire2 (1985), pp. 1-20. Zbl0601.60076MR781589
  5. [5] W.H. Fleming, Exit probabilities and stochastic optimal control, Appl. Math. Optim.4 (1978), pp. 329-346. Zbl0398.93068MR512217
  6. [6] M.I. Freidlin, A.D. Wentzell, Random perturbations of dynamical systems, Springer-Verlag, New York1984. Zbl0922.60006MR722136
  7. [7] A. Friedman, Small random perturbations of dynamical systems and applications to parabolic equations, Indiana Univ. Math. J.24 (1974), pp. 533-553; Erratum, ibid. 24 (1975), p. 903. Zbl0306.60034MR368190
  8. [8] A. Friedman, Stochastic differential equations and applications, Vol. 2, Academic Press, New York1976. Zbl0323.60057MR494491
  9. [9] D. Gilbarg, N.S. Trudinger, Elliptic partial differential equations of second order, 2nd edition, Springer-Verlag, Berlin1983. Zbl0562.35001MR737190
  10. [10] M. Grüter, K.O. Widman, The Green function for uniformly elliptic equations, Manuscripta Math.37 (1982), pp. 303-342. Zbl0485.35031MR657523
  11. [11] S. Kamin, On elliptic singular perturbation problems with several turning points, in: Theory and applications of singular perturbations, W. Eckhaus and E.M. de Jager eds., Lecture Notes in Math. 942, Springer-Verlag1982. Zbl0507.35005
  12. [12] S. Kamin, Exponential descent of solutions of elliptic singular perturbation problems, Comm. Partial Differential Equations9 (1984), pp. 197-213. Zbl0541.35025MR736415
  13. [13] N. Levinson, The first boundary value problem for ε Δu + A(x, y)ux + B (x, y)uy + C (x,y)u = D (x, y) for small ε, Ann. of Math.51 (1950), pp. 428-445. Zbl0036.06801
  14. [14] P.L. Lions, Generalized solutions of Hamilton-Jacobi equations, Pitman, Boston1982. Zbl0497.35001MR667669
  15. [15] Z. Schuss, Singular perturbation methods in stochastic differential equations of mathematical physics, SIAM Rev.22 (1980), pp. 119-155. Zbl0436.60045MR564560
  16. [16] G. Stampacchia, Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier (Grenoble) 15 (1965), pp. 189-258. Zbl0151.15401MR192177
  17. [17] S.R.S. Varadhan, On the behavior of the fundamental solution of the heat equation with variable coefficients, Comm. Pure Appl. Math.20 (1967), pp. 431-455. Zbl0155.16503MR208191
  18. [18] S.R.S. Varadhan, Diffusion processes in a small time interval, Comm. Pure Appl. Math.20 (1967), pp. 659-685. Zbl0278.60051MR217881
  19. [19] S. Kamin, Singular perturbation problems and the Hamilton-Jacobi equation, Integral Equations Operator Theory9 (1986), pp. 95-105. Zbl0599.70030MR824621

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