Tho, Nguyen HuuVan, Tran Duc2020-11-242020-11-242003-05-21Tho, N. H., & Van, T. D. (2003). Hopf-type estimates for solutions to Hamilton-Jacobi equations with concave-convex initial data. <i>Electronic Journal of Differential Equations, 2003</i>(59), pp. 1-11.1072-6691https://hdl.handle.net/10877/12999We 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.Text11 pages1 file (.pdf)enAttribution 4.0 InternationalHamilton-Jacobi equationsHopf-type formulaGlobal Lipschitz solutionsViscosity solutionsHopf-type estimates for solutions to Hamilton-Jacobi equations with concave-convex initial dataArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.