Work

Continuous dependence estimates for viscosity solutions of fully nonlinear degenerate elliptic equations

Year: 2001

Type: report

Abstract: Using the maximum principle for semicontinuousfunctions [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.

Source: NORA - Norwegian Open Research Archives

Authors: Jakobsen, Espen R., Karlsen, Kenneth Hvistendahl

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W3138957103

Cites:

Cited by: 33

Related to: 9