Continuous Dependence Estimates for Viscosity Solutions of Fully Nonlinear Degenerate Elliptic Equations

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dc.contributor.authorJakobsen, Espen R.
dc.contributor.authorKarlsen, Kenneth H.
dc.date.accessioned2020-08-05T19:37:28Z
dc.date.available2020-08-05T19:37:28Z
dc.date.issued2002-05-06
dc.description.abstractUsing 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.
dc.description.departmentMathematics
dc.formatText
dc.format.extent10 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationJakobsen, 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.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/12313
dc.language.isoen
dc.publisherSouthwest Texas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2002, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectFully nonlinear degenerate elliptic equation
dc.subjectViscosity solution
dc.subjectHamilton-Jacobi-Bellman-Isaacs equation
dc.subjectContinuous dependence estimate
dc.subjectVanishing viscosity method
dc.subjectConvergence rate
dc.titleContinuous Dependence Estimates for Viscosity Solutions of Fully Nonlinear Degenerate Elliptic Equationsen_US
dc.typeArticle

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