Hopf-type formula defines viscosity solution for Hamilton-Jacobi equations with -dependence Hamiltonian

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• 作者：Nguyen Hoang ; ^{nguyenhoanghue@gmail.com} ; ^{hoangboi2000@yahoo.com} ; ^{nguyenhoang@hueuni.edu.vn}
• 关键词：Hamilton&ndash ; Jacobi equation ; Hopf-type formula ; Viscosity solution ; Semiconvexity
• 刊名：Nonlinear Analysis
• 出版年：2012
• 期刊代码：43_0362546x
• 类别：mt
• 出版时间：May, 2012
• 卷：75
• 期：8
• 页码：3543-3551
• 文件大小：230 K

摘要

We prove that under some assumptions, the Hopf-type formula defines a viscosity solution of the Cauchy problem for Hamilton-Jacobi equation where the initial condition is convex but the Hamiltonian is not necessarily convex in .