Geodesic
Continuous dependence estimates for viscosity solutions of fully nonlinear degenerate elliptic equations
Electronic Journal of Differential Equations, Tome 2002 (2002).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 35J60, 35J70, 49L25
Keywords: fully nonlinear degenerate elliptic equation, viscosity solution, Hamilton-Jacobi-bellman-isaacs equation, continuous dependence estimate, vanishing viscosity method 
@article{EJDE_2002__2002__a167,
     author = {Jakobsen, Espen R. and Karlsen, Kenneth H.},
     title = {Continuous dependence estimates for viscosity solutions of fully nonlinear degenerate elliptic equations},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2002},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a167/}
}
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Jakobsen, Espen R.; Karlsen, Kenneth H. Continuous dependence estimates for viscosity solutions of fully nonlinear degenerate elliptic equations. Electronic Journal of Differential Equations, Tome 2002 (2002). http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a167/