ON EXPLICIT VISCOSITY SOLUTIONS TO NONCONVEX-NONCONCAVE HAMILTON-JACOBI EQUATIONS
TRAN DUC VAN, MAI DUC THANH
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-Oleinik-Lax-type formulas for viscosity sub- and super-solutions are presented. A sharp estimate for the unique viscosity solution is established.
Viện Toán học, Viện Hàn lâm Khoa học và Công nghệ Việt Nam
Địa chỉ: Số 18 đường Hoàng Quốc Việt, quận Cầu Giấy, Hà Nội
Điện thoại: 024 37563474 - Fax: 024 37564303
Email: vientoan@math.ac.vn
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