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
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.
Submitted August 8, 2001. Published May 6, 2002.
Math Subject Classifications: 35J60, 35J70, 49L25.
Key Words: fully nonlinear degenerate elliptic equation,
viscosity solution,
Hamilton-Jacobi-Bellman-Isaacs 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 N-7491 Trondheim, Norway e-mail: erj@math.ntnu.no http://www.math.ntnu.no/~erj |
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Kenneth H. Karlsen Department of Mathematics University of Bergen Johs. Brunsgt. 12 N-5008 Bergen, Norway e-mail: kennethk@mi.uib.no http://www.mi.uib.no/~kennethk |
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