Application of Lipschitz viscosity solutions for higher-order partial differential equations containing the special Lagrangian operator
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Abstract
Using the Lipschitz continuity of a class of viscosity solutions, we find a kind of viscosity solution for some higher-order partial differential equations containing the special Lagrangian operator. Additionally, we extend this analysis to equations that simultaneously contain the special Lagrangian and some other operators including Laplacian.
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References
Luigi . Ambrosio and Carlotto. Alessandro and Massaccesi. Annalisa, Lectures on elliptic partial differential equations, Vol. 18, Springer, 2019.
M.P. Coiculescu, An Application of the Theory of Viscosity Solutions to Higher Order Differential Equations, Monatshefte fur Mathematik, 203 (2024), 825–841.
M.G. Crandall and H. Ishii and P.L. Lions, User’s guide to Viscosity Solutions of Second Order Partial Differential Equations, Bull. Amer. Math. Soc., 27.1 (1992), 11 1–67.
W. Hackbusch, Elliptic Differential Equations, Springer Series in Computational Mathematics, Vol. 18, Springer, 2017.
H. Ishii and P.L. Lions, Viscosity Solutions of Fully Nonlinear Second-Order Elliptic Partial Differential Equations, Journal of Differential Equations, 83.1 (1990), 26–78.
E. Jakobsen and K. Karlsen, Continuous Dependence Estimates for Viscosity Solutions of Fully Nonlinear Degenerate Elliptic Equations, Electronic Journal of Differential Equations, 2002 (2002), 1–10.
R. Jensen and P.E. Souganidis, A Regularity Result for Viscosity Solutions of Hamilton-Jacobi Equations in One Space Dimension, Trans. Amer. Math. Soc., 301.1 (1987), 137–147.
C. Mooney and O. Savin, Non C1 solutions to the special Lagrangian equation, Equations in One Space Dimension, Duke Mathematical Journal, 1.1 (2024), 1–17.