Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Estimates for viscosity solutions of parabolic equations with Dirichlet boundary conditions

Author(s): G. Gripenberg
Journal: Proc. Amer. Math. Soc. 130 (2002), 3651-3660.
MSC (2000): Primary 35K55, 35K65, 35K20
Posted: May 1, 2002
Retrieve article in: PDF DVI PostScript
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: It is shown how one can get upper bounds for $\lvert u-v \rvert$when $u$ and $v$ are the (viscosity) solutions of

\begin{displaymath}u_t - \alpha(D_x u) \Delta_x u = 0\quad\text{and}\quad v_t - \beta(D_x v) \Delta_x v = 0, \end{displaymath}

respectively, in $(0,\infty)\times \Omega$ with Dirichlet boundary conditions. Similar results are obtained for some other parabolic equations as well, including certain equations in divergence form.

References:

1.
B. Cockburn, G. Gripenberg, and S-O. Londen.
Continuous dependence on the nonlinearity of viscosity solutions of parabolic equations.
J. Differential Equations, 170:180-187, 2001. CMP 2001:08

2.
M. G. Crandall.
Viscosity solutions: a primer.
In Viscosity solutions and applications (Montecatini Terme, 1995), volume 1660 of Lecture Notes in Math., pages 1-43. Springer, Berlin, 1997. MR 98g:35034

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., 27:1-67, 1992. MR 92j:35050

4.
D. Nunziante.
Existence and uniqueness of unbounded viscosity solutions of parabolic equations with discontinuous time-dependence.
Nonlinear Anal., 18(11):1033-1062, 1992. MR 93f:35125

5.
T. Rockafellar.
Convex analysis.
Princeton University Press, Princeton, N.J., 1970. MR 43:445

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35K55, 35K65, 35K20

Retrieve articles in all Journals with MSC (2000): 35K55, 35K65, 35K20

Additional Information:

G. Gripenberg
Affiliation: Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100, FIN-02015 HUT, Finland
Email: gustaf.gripenberg@hut.fi

DOI: 10.1090/S0002-9939-02-06580-2
PII: S 0002-9939(02)06580-2
Keywords: Viscosity solution, parabolic, dependence on data, Dirichlet boundary condition
Received by editor(s): July 23, 2001
Posted: May 1, 2002
Communicated by: David S. Tartakoff
Copyright of article: Copyright 2002, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google