Continuous Dependence Estimates for Viscosity Solutions of Fully Nonlinear Degenerate Elliptic Equations
Date
2002-05-06
Authors
Jakobsen, Espen R.
Karlsen, Kenneth H.
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
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.
Description
Keywords
Fully nonlinear degenerate elliptic equation, Viscosity solution, Hamilton-Jacobi-Bellman-Isaacs equation, Continuous dependence estimate, Vanishing viscosity method, Convergence rate
Citation
Jakobsen, E. R., & Karlsen, K. H. (2002). Continuous dependence estimates for viscosity solutions of fully nonlinear degenerate elliptic equations. <i>Electronic Journal of Differential Equations, 2002</i>(39), pp. 1-10.
Rights
Attribution 4.0 International