Duke Mathematical Journal

Fully nonlinear oblique derivative problems for nonlinear second-order elliptic PDE’s

Hitoshi Ishii

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Article information

Source
Duke Math. J. Volume 62, Number 3 (1991), 633-661.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077296510

Digital Object Identifier
doi:10.1215/S0012-7094-91-06228-9

Mathematical Reviews number (MathSciNet)
MR1104812

Zentralblatt MATH identifier
0733.35020

Subjects
Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations

Citation

Ishii, Hitoshi. Fully nonlinear oblique derivative problems for nonlinear second-order elliptic PDE’s. Duke Math. J. 62 (1991), no. 3, 633--661. doi:10.1215/S0012-7094-91-06228-9. http://projecteuclid.org/euclid.dmj/1077296510.


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References

  • [1] M. G. Crandall, Semidifferentials, quadratic forms and fully nonlinear elliptic equations of second order, Ann. Inst. H. Poincaré Anal. Non Linéaire 6 (1989), no. 6, 419–435.
  • [2] M. G. Crandall and H. Ishii, The maximum principle for semicontinuous functions, preprint.
  • [3] M. G. Crandall and P.-L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 277 (1983), no. 1, 1–42.
  • [4] P. Dupuis and H. Ishii, On oblique derivative problems for fully nonlinear second-order elliptic PDE's on nonsmooth domains, to appear in Nonlinear Anal.
  • [5] P. Dupuis and H. Ishii, On oblique derivative problems for fully nonlinear second-order elliptic PDE's domains with corners, preprint.
  • [6] P. Dupuis, H. Ishii, and H. M. Soner, A viscosity solution approach to the asymptotic analysis of queuing systems, To appear in Ann. Prob.
  • [7] W. H. Fleming, H. Ishii, and J.-L. Menaldi, work in preparation.
  • [8] D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, 2nd ed. ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 224, Springer-Verlag, Berlin, 1983.
  • [9] H. Ishii, Perron's method for Hamilton-Jacobi equations, Duke Math. J. 55 (1987), no. 2, 369–384.
  • [10] H. Ishii, A boundary value problem of the Dirichlet type for Hamilton-Jacobi equations, to appear in Ann. Scula Norm. Sup. Pisa. (IV) 16 (1989), 105–135.
  • [11] H. Ishii, On uniqueness and existence of viscosity solutions of fully nonlinear second-order elliptic PDEs, Comm. Pure Appl. Math. 42 (1989), no. 1, 15–45.
  • [12] H. Ishii and P.-L. Lions, Viscosity solutions of fully nonlinear second-order elliptic partial differential equations, J. Differential Equations 83 (1990), no. 1, 26–78.
  • [13] R. Jensen, The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations, Arch. Rational Mech. Anal. 101 (1988), no. 1, 1–27.
  • [14] R. Jensen, Uniqueness criteria for viscosity solutions of fully nonlinear elliptic partial differential equations, Indiana Univ. Math. J. 38 (1989), no. 3, 629–667.
  • [15] R. Jensen, P.-L. Lions, and P. E. Souganidis, A uniqueness result for viscosity solutions of second order fully nonlinear partial differential equations, Proc. Amer. Math. Soc. 102 (1988), no. 4, 975–978.
  • [16] P.-L. Lions, Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations. II. Viscosity solutions and uniqueness, Comm. Partial Differential Equations 8 (1983), no. 11, 1229–1276.
  • [17] P.-L. Lions, Neumann type boundary conditions for Hamilton-Jacobi equations, Duke Math. J. 52 (1985), no. 4, 793–820.
  • [18] P.-L. Lions and N. S. Trudinger, Linear oblique derivative problems for the uniformly elliptic Hamilton-Jacobi-Bellman equation, Math. Z. 191 (1986), no. 1, 1–15.