发表机构
Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对有界凸域中带Neumann型边界条件的一阶Hamilton-Jacobi发展方程，利用凸包论证证明其粘性解的空间凸性保持，并得到半凸性与强凸性的传播估计。
AI 中文摘要
我们研究有界凸域中带Neumann型边界条件的一阶Hamilton-Jacobi发展方程的粘性解的空间凸性保持问题。在哈密顿量关于外法向满足单调性假设的条件下，Neumann问题的每个粘性上解同时也是状态约束上解，这将边界困难简化为状态约束问题，使我们能通过Alvarez、Lasry和Lions（1997）建立的凸包论证证明凸性保持。我们还在类似结构假设下得到半凸性和强凸性的传播估计。
英文摘要
We study preservation of spatial convexity for viscosity solutions of first order Hamilton-Jacobi evolution equations with Neumann-type boundary conditions in bounded convex domains. Under a monotonicity assumption on the Hamiltonian in the outward normal direction, every viscosity supersolution of the Neumann problem is also a state-constraint supersolution. This reduces the boundary difficulty to a state-constraint problem and enables us to prove convexity preservation via the convex-envelope argument established by Alvarez, Lasry and Lions (1997). We also obtain propagation estimates for semiconvexity and strong convexity under similar structural assumptions.
