论文标题
半线性汉密尔顿 - 雅各比方程的解决方案的限制，具有退化粘度
Limit of solutions for semilinear Hamilton-Jacobi equations with degenerate viscosity
论文作者
论文摘要
在本文中，我们证明了粘度解决方案$u_λ$的收敛性为$λ\ rightArrow0 _+$，用于参数化的退化粘性hamilton-jacobi方程\ [H（x，d_x u，λu）=α（x）=α（x）ΔU，\ quadα（x）Δ $ H：T^*M \ Times \ Mathbb r \ rightarrow \ Mathbb r $上的凸和单调条件。这种极限可以以与关键方程相关的随机马瑟测量为特征。 \]
In the paper we prove the convergence of viscosity solutions $u_λ$ as $λ\rightarrow0_+$ for the parametrized degenerate viscous Hamilton-Jacobi equation \[ H(x,d_x u, λu)=α(x)Δu,\quad α(x)\geq 0,\quad x\in \mathbb T^n \] under suitable convex and monotonic conditions on $H: T^*M\times\mathbb R\rightarrow\mathbb R$. Such a limit can be characterized in terms of stochastic Mather measures associated with the critical equation \[ H(x,d_x u,0)=α(x)Δu. \]
