Electron. J. Diff. Eqns., Vol. 2003(2003), No. 59, pp. 1-11.

Hopf-type estimates for solutions to Hamilton-Jacobi equations with concave-convex initial data

Nguyen Huu Tho & Tran Duc Van

We consider the Cauchy problem for the Hamilton-Jacobi equations with concave-convex initial data. A Hopf-type formula for global Lipschitz solutions and estimates for viscosity solutions of this problem are obtained using techniques of multifunctions and convex analysis.

Submitted July 3, 2002. Published May 21, 2003.
Math Subject Classifications: 35A05, 35F20, 35F25.
Key Words: Hamilton-Jacobi equations, Hopf-type formula, global Lipschitz solutions, viscosity solutions.

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Nguyen Huu Tho
Bureau of Education and Training of Hatay
Tran Duc Van
Hanoi Institute of Mathematics
P.O. Box 631, BoHo, Hanoi, Vietnam
email: tdvan@thevinh.ac.vn

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