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viscosity subsolution; viscosity supersolution; mean curvature equation; pseudo $p$-Laplace equation

References:

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[2] Chen, Y. G., Giga, Y., Goto, S.: **Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations**. J. Differential Geom. 33 (1991), 749–786. MR 1100211 | Zbl 0696.35087

[3] Crandall, M., Kocan, M., Lions, P. L., Swiȩch, A.: **Existence results for uniformly elliptic and parabolic fully nonlinear equations**. Electron. J. Differential Equations 24 (1999), 1–20.

[4] Crandall, M. G., Ishii, H., Lions, P. L.: **User’s guide to viscosity solutions of second order partial differential equations**. Bull. Amer. Math. Soc. 27 (1992), 1–67. DOI 10.1090/S0273-0979-1992-00266-5 | MR 1118699 | Zbl 0755.35015

[5] Crandall, M. G., Lions, P. L.: **Viscosity solutions of Hamilton-Jacobi equations**. Trans. Amer. Math. Soc. 277 (1983), 1–42. DOI 10.1090/S0002-9947-1983-0690039-8 | MR 0690039 | Zbl 0599.35024

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[7] Kawohl, B., Kutev, N.: **Comparison principle and Lipschitz regularity for viscosity solutions of some classes of nonlinear partial differential equations**. Funkcial. Ekvac. 43 (2000), 241–253. MR 1795972 | Zbl 1142.35315

[8] Tersenov, Al., Tersenov, Ar.: **Viscosity solutions of $p$-Laplace equation with nonlinear source**. Arch. Math. (Basel) 88 (3) (2007), 259–268. DOI 10.1007/s00013-006-1873-9 | MR 2305604

[9] Trudinger, N. S.: **Holder gradient estimates for fully nonlinear elliptic equations**. Proc. Roy. Soc. Edinburgh Sect. A 108 (1988), 57–65. MR 0931007