References
- Chen Y-G, Giga Y, Goto S. Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations. J Differ Geom. 1991;33(3):749–786. doi: 10.4310/jdg/1214446564
- Evans LC, Spruck J. Motion of level sets by mean curvature. I. J Differ Geom. 1991;33(3):635–681. doi: 10.4310/jdg/1214446559
- Giga Y. Surface evolution equations: a level set approach. Basel: Birkhauser Verlag; 2006. (Monographs in Mathematics; 99).
- Sussman M, Fatemi E. An efficient, interface-preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow. SIAM J Sci Comput. 1999;20(4):1165–1191. doi: 10.1137/S1064827596298245
- Sussman M, Smereka P, Osher S. A level set approach for computing solutions to incompressible two-phase flow. J Comput Phys. 1994;114(1):146–159. doi: 10.1006/jcph.1994.1155
- Roisman I. Implicit surface method for numerical simulations of moving interfaces, Lecture at the International Workshop on ‘Transport Processes at Fluidic Interfaces from Experimental to Mathematical Analysis’; 2011 December 5–7; Aachen, Germany.
- Barles G. Uniqueness and regularity results for first-order Hamilton–Jacobi equations. Indiana Univ Math J. 1990;39(2):443–466. doi: 10.1512/iumj.1990.39.39024
- Ley O. Lower-bound gradient estimates for first-order Hamilton–Jacobi equations and applications to the regularity of propagating fronts. Adv Differ Equ. 2001;6(5):547–576.
- Fujita Y. Lower estimates of L∞-norm of gradients for Cauchy problems. J Math Anal Appl. 2018;458(2):910–924. doi: 10.1016/j.jmaa.2017.08.045
- Hamamuki N, Ntovoris E. A rigorous setting for the reinitialization of first order level set equations. Interfaces Free Bound. 2016;18(4):579–621. doi: 10.4171/IFB/374
- Hamamuki N. A few topics related to maximum principles [Ph.D. thesis]. University of Tokyo; 2013.
- Hamamuki N. An improved level set method for Hamilton–Jacobi equations, RIMS Kokyuroku, No. 1962. 2015, p. 27–44. (Japanese).
- Crandall MG, Ishii H, Lions PL. User's guide to viscosity solutions of second order partial differential equations. Bull Amer Math Soc (N.S.). 1992;27(1):1–68. doi: 10.1090/S0273-0979-1992-00266-5
- Kimura M. Geometry of hypersurfaces and moving hypersurfaces in Rm for the study of moving boundary problems, Topics in mathematical modeling. Prague: Matfyzpress; 2008. p. 39–93, Jindřich Nečas Cent. Math. Model. Lect. Notes; 4.
- Evans LC, Soner HM, Souganidis PE. Phase transitions and generalized motion by mean curvature. Comm Pure Appl Math. 1992;45(9):1097–1123. doi: 10.1002/cpa.3160450903
- Bardi M, Capuzzo-Dolcetta I. Optimal control and viscosity solutions of Hamilton–Jacobi–Bellman equations. With appendices by Maurizio Falcone and Pierpaolo Soravia. Boston (MA): Systems & Control: Foundations & Applications, Birkhäuser Boston, Inc.; 1997.
- Pironneau O. Finite element methods for fluids. Translated from the French. Chichester/Paris: John Wiley & Sons/Masson; 1989.