Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 59, pp. 1-11.

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

Authors: Nguyen Huu Tho (Bureau of Education, Vietnam)
         Tran Duc Van (Hanoi Institute of Math., Vietnam)

Abstract: 
 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