论文标题
粘性HJ方程的离散近似
Discrete approximation of the viscous HJ equation
论文作者
论文摘要
我们考虑在动量变量中，固定粘性的汉密尔顿雅各布方程的随机离散化与哈密顿，凸和超线性有关。我们表明，每个离散问题都允许在圆环上进行独特的连续解决方案，直到添加剂常数为止。另外，通过假设相关的拉格朗日的技术条件，我们表明粘性汉密尔顿雅各比方程的每个解决方案都是离散问题的解决方案的限制，因为离散化步骤为零。
We consider a stochastic discretization of the stationary viscous Hamilton Jacobi equation on the flat d dimensional torus, associated with a Hamiltonian, convex and superlinear in the momentum variable. We show that each discrete problem admits a unique continuous solution on the torus, up to additive constants. By additionally assuming a technical condition on the associated Lagrangian, we show that each solution of the viscous Hamilton Jacobi equation is the limit of solutions of the discrete problems, as the discretization step goes to zero.
