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Vietnam Journal of Mathematics 34:2(2006) 209-239

 Hopf-Lax-Oleinik-Type Estimates for Viscosity Solutions to Hamilton-Jacobi Equations with Concave-Convex Data

Tran Duc Van and Nguyen Duy Thai Son

Abstract.  We consider the Cauchy problem to Hamilton-Jacobi equations with either concave-convex Hamiltonian or concave-convex initial data and investigate their explicit viscosity solutions in connection with Hopf-Lax-Oleinik-type estimates.

2000 Mathematics Subject Classification: 35A05, 35F20, 35F25.

Keywords: Hopf-Lax-Oleinik-type estimates, Viscosity solutions, Concave-convex function, Hamilton-Jacobi equations.

Established by Vietnam Academy of Science and Technology & Vietnam Mathematical Society

Published by Springer since January 2013