Fully nonlinear oblique derivative problems for nonlinear second-order elliptic PDE’s
Log in :: RSS/Atom Feeds
Duke Mathematical Journal

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

Hitoshi Ishii

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

First Page PDF: View first page of article (PDF, 78 KB)

Primary Subjects: 35J65

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Alternatively, the document is available for a cost of $25. Select the "buy article" button below to purchase this document from a secured VeriSign, Inc. site.
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077296510
Mathematical Reviews number (MathSciNet): MR1104812
Zentralblatt MATH identifier: 0733.35020
Digital Object Identifier: doi:10.1215/S0012-7094-91-06228-9

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.
Mathematical Reviews (MathSciNet): MR91i:35072
Zentralblatt MATH: 0734.35033
[2] M. G. Crandall and H. Ishii, The maximum principle for semicontinuous functions, preprint.
Mathematical Reviews (MathSciNet): MR1073054
[3] M. G. Crandall and P.-L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 277 (1983), no. 1, 1–42.
Mathematical Reviews (MathSciNet): MR85g:35029
Zentralblatt MATH: 0599.35024
Digital Object Identifier: doi:10.2307/1999343
[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.
Mathematical Reviews (MathSciNet): MR1082287
[5] P. Dupuis and H. Ishii, On oblique derivative problems for fully nonlinear second-order elliptic PDE's domains with corners, preprint.
Mathematical Reviews (MathSciNet): MR1096165
[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.
Mathematical Reviews (MathSciNet): MR1043946
JSTOR: links.jstor.org
[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.
Mathematical Reviews (MathSciNet): MR86c:35035
Zentralblatt MATH: 0562.35001
[9] H. Ishii, Perron's method for Hamilton-Jacobi equations, Duke Math. J. 55 (1987), no. 2, 369–384.
Mathematical Reviews (MathSciNet): MR89a:35053
Zentralblatt MATH: 0697.35030
Digital Object Identifier: doi:10.1215/S0012-7094-87-05521-9
Project Euclid: euclid.dmj/1077306027
[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.
Mathematical Reviews (MathSciNet): MR1056130
[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.
Mathematical Reviews (MathSciNet): MR89m:35070
Zentralblatt MATH: 0645.35025
[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.
Mathematical Reviews (MathSciNet): MR90m:35015
Zentralblatt MATH: 0708.35031
Digital Object Identifier: doi:10.1016/0022-0396(90)90068-Z
[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.
Mathematical Reviews (MathSciNet): MR89a:35038
Zentralblatt MATH: 0708.35019
Digital Object Identifier: doi:10.1007/BF00281780
[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.
Mathematical Reviews (MathSciNet): MR91f:35098
Zentralblatt MATH: 0838.35037
Digital Object Identifier: doi:10.1512/iumj.1989.38.38030
[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.
Mathematical Reviews (MathSciNet): MR89f:35027
Zentralblatt MATH: 0662.35048
Digital Object Identifier: doi:10.2307/2047344
[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.
Mathematical Reviews (MathSciNet): MR85i:49043b
Zentralblatt MATH: 0716.49023
[17] P.-L. Lions, Neumann type boundary conditions for Hamilton-Jacobi equations, Duke Math. J. 52 (1985), no. 4, 793–820.
Mathematical Reviews (MathSciNet): MR87h:35055
Zentralblatt MATH: 0599.35025
Digital Object Identifier: doi:10.1215/S0012-7094-85-05242-1
Project Euclid: euclid.dmj/1077304723
[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.
Mathematical Reviews (MathSciNet): MR87e:35041
Zentralblatt MATH: 0593.35046
Digital Object Identifier: doi:10.1007/BF01163605

2008 © Duke University Press