Sci Math | On explicit viscosity solutions to nonconvex-nonconcave Hamilton-Jacobi equations

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On explicit viscosity solutions to nonconvex-nonconcave Hamilton-Jacobi equations

Authors: Trần Đức Vân, Mai Đức Thành,

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Publisher, magazine: ,

Publication year: 2001

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Abstract

We consider the Cauchy problem for Hamilton-Jacobi equations in the case where the Hamiltonian is supposed to be a sum of a convex and a concave function and to depend also on the unknown function. Hopf-OleinikLax-type formulas for viscosity sub- and super-solutions are presented. A sharp estimate for the unique viscosity solution is established.

Tags: Hopf-Oleinik-Lax-type formulas, viscosity solutions, HamiltonJacobi equations, quasiconvex dual, nonconvex-nonconcave functions

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