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Harnack's inequality for viscosity solutions to degenerate elliptic equations in two variables
Author(s):
G.
Gripenberg
Journal:
Proc. Amer. Math. Soc.
137
(2009),
3703-3708.
MSC (2000):
Primary 35J60
Posted:
June 25, 2009
MathSciNet review:
2529877
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Abstract:
A Harnack inequality is established for viscosity solutions to the elliptic equation  in two variables.
References:
-
- 1.
- G. Barles and J. Busca.
Existence and comparison results for fully nonlinear degenerate elliptic equations without zeroth-order term.
Comm. Partial Differential Equations, 26(11-12):2323-2337, 2001. MR 1876420 (2002k:35078) - 2.
- L.A. Caffarelli and X. Cabré.
Fully nonlinear elliptic equations. Volume 43 of American Mathematical Society Colloquium Publications.
American Mathematical Society, Providence, RI, 1995. MR 1351007 (96h:35046) - 3.
- M.G. Crandall, H. Ishii, and P.L. Lions.
User's guide to viscosity solutions of second order partial differential equations.
Bull. Amer. Math. Soc. (N.S.), 27:1-67, 1992. MR 1118699 (92j:35050) - 4.
- D. Gilbarg and N.S. Trudinger.
Elliptic partial differential equations of second order.
Classics in Mathematics. Springer-Verlag, Berlin, 2001.
Reprint of the 1998 edition. MR 1814364 (2001k:35004)
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Additional Information:
G.
Gripenberg
Affiliation:
Department of Mathematics and Systems Analysis, Helsinki University of Technology, P.O. Box 1100, FIN-02015 TKK, Finland
Email:
gustaf.gripenberg@tkk.fi
DOI:
10.1090/S0002-9939-09-10030-8
PII:
S 0002-9939(09)10030-8
Keywords:
Harnack's inequality,
viscosity solution
Received by editor(s):
August 21, 2008
Posted:
June 25, 2009
Communicated by:
Matthew J. Gursky
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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