具有非线性Neumann边界条件和可测系数的PDE的惩罚
Penalization for a PDE with a Nonlinear Neumann boundary condition and measurable coefficients *
摘要：
本文考虑一个具有可测系数和非线性Neumann边界条件的半线性偏微分方程组。然后，我们构造了一系列的惩罚偏微分方程收敛到我们的初始问题的解决方案。我们构造的解决方案是在Lp-粘性意义下，因为系数可以是不连续的。我们使用的方法是基于倒向随机微分方程及其S-紧性。物理学中的许多偏微分方程具有不连续系数，这是本文工作的出发点。
英文摘要：
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.
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