Electron. J. Diff. Eqns., Vol. 2002(2002), No. 39, pp. 110.
Continuous dependence estimates for viscosity solutions of
fully nonlinear degenerate elliptic equations
Espen R. Jakobsen & Kenneth H. Karlsen
Abstract:
Using the maximum principle for semicontinuous
functions [3,4], we prove a general
``continuous dependence on the nonlinearities''
estimate for bounded Holder continuous viscosity solutions
of fully nonlinear degenerate elliptic equations.
Furthermore, we provide existence, uniqueness, and Holder
continuity results for bounded viscosity solutions of such
equations. Our results are general enough to encompass
HamiltonJacobiBellmanIsaacs's equations of zerosum, twoplayer
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.
Submitted August 8, 2001. Published May 6, 2002.
Math Subject Classifications: 35J60, 35J70, 49L25.
Key Words: fully nonlinear degenerate elliptic equation,
viscosity solution,
HamiltonJacobiBellmanIsaacs equation,
continuous dependence estimate, vanishing viscosity method,
convergence rate
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Espen R. Jakobsen
Department of Mathematical Sciences
Norwegian University of Science and Technology
N7491 Trondheim, Norway
email: erj@math.ntnu.no
http://www.math.ntnu.no/~erj 

Kenneth H. Karlsen
Department of Mathematics
University of Bergen
Johs. Brunsgt. 12
N5008 Bergen, Norway
email: kennethk@mi.uib.no
http://www.mi.uib.no/~kennethk 
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