论文标题
对具有非线性Neumann边界条件和可测量系数的PDE进行惩罚 *
Penalization for a PDE with a Nonlinear Neumann boundary condition and measurable coefficients *
论文作者
论文摘要
我们考虑具有可测量系数和非线性诺伊曼边界条件的半线性部分微分方程的系统。然后，我们构建了一系列受惩罚的部分微分方程，该方程会收敛到我们最初问题的解决方案。我们构建的解决方案是在l p粘度意义上，因为系数可能不是连续的。我们使用的方法是基于向后的随机微分方程及其Stightness。目前的工作是由于物理学中出现的许多偏微分方程具有不连续系数的事实。
We consider a system of semi-linear partial differential equations with measurable coefficients and a nonlinear Neumann boundary condition. We then construct a sequence of penalized partial differential equations which converges to a solution of our initial problem. The solution we construct is in the L p --viscosity sense, since the coefficients can be not continuous. The method we use is based on backward stochastic differential equations and their S-tightness. The present work is motivated by the fact that many partial differential equations arising in physics have discontinuous coefficients.
