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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Estimates for viscosity solutions of parabolic equations with Dirichlet boundary conditions


Author: G. Gripenberg
Journal: Proc. Amer. Math. Soc. 130 (2002), 3651-3660
MSC (2000): Primary 35K55, 35K65, 35K20
Published electronically: May 1, 2002
MathSciNet review: 1920045
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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.


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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: http://dx.doi.org/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
Published electronically: May 1, 2002
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2002 American Mathematical Society