论文标题
汉密尔顿折扣折扣 - 雅各比方程的解决方案的融合
Convergence of solutions for some degenerate discounted Hamilton--Jacobi equations
论文作者
论文摘要
我们研究汉密尔顿的解决方案 - 形式的jacobi方程$$λα（x）u_λ（x） + h（x，d_xu_λ）= c，$$ 其中$α$是一种非负功能，$λ$一个正常数，$ c $ a nistance $ h $ a凸强制性哈密顿量。在$α$的适当条件下，我们证明函数$u_λ$收敛为$λ\ to 0 $ to函数$ u_0 $，这是关键方程$ h（x，d_x u_0）= c $的解决方案。
We study solutions of Hamilton--Jacobi equations of the form $$λα(x) u_λ(x) + H(x, D_x u_λ) = c,$$ where $α$ is a nonnegative function, $λ$ a positive constant, $c$ a constant and $H $ a convex coercive Hamiltonian. Under suitable conditions on $α$ we prove that the functions $u_λ$ converge as $λ\to 0$ to a function $u_0$ that is a solution of the critical equation $H(x, D_x u_0) = c$.
