Preprint 2001-029

Continuous Dependence Estimates for Viscosity Solutions of Fully Nonlinear Degenerate Elliptic Equations

Espen R. Jakobsen and Kenneth Hvistendahl Karlsen

Abstract: Using the maximum principle for semicontinuous functions \cite{CrIs:MaxPrinc,CrIsLi:UserGuide}, we prove a general ``continuous dependence on the nonlinearities'' estimate for bounded H\"{o}lder continuous viscosity solutions of fully nonlinear degenerate elliptic equations. Furthermore, we provide existence, uniqueness, and H\"{o}lder continuity results for bounded viscosity solutions of such equations. Our results are general enough to encompass Hamilton-Jacobi-Bellman-Isaacs's equations of zero-sum, two-player stochastic differential games. An immediate consequence of the results obtained herein is a rate of convergence for the vanishing viscosity method for fully nonlinear degenerate elliptic equations.

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Espen R. Jakobsen, <>
Kenneth Hvistendahl Karlsen, <>
Publishing information:
Appeared in: Electron. J. Diff. Eqns. Vol. 2002(2002), No. 39, pp. 1-10.
Some correction has been made in the published version.
Submitted by:
<> July 17 2001.

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