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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 |
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Tran Duc Van and Nguyen Duy Thai Son |
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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. |
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2000 Mathematics Subject Classification: 35A05, 35F20, 35F25. |
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Keywords: Hopf-Lax-Oleinik-type estimates, Viscosity solutions, Concave-convex function, Hamilton-Jacobi equations. |
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