论文标题
完全非线性抛物线方程的连续性估计模量
Modulus of Continuity Estimates for Fully Nonlinear Parabolic Equations
论文作者
论文摘要
我们证明，对完全非线性抛物线偏微分方程的粘度解决方案连续性的模量是一个空间变量的合适抛物线方程的粘度亚物种。作为应用，我们通过与一维溶液进行比较，获得具有有界初始数据的完全非线性抛物线方程的尖锐的Lipschitz边界和梯度估计值。这项工作扩展了Andrews and Clutterbuck的准线性方程式的多个结果。
We prove that the moduli of continuity of viscosity solutions to fully nonlinear parabolic partial differential equations are viscosity subsolutions of suitable parabolic equations of one space variable. As applications, we obtain sharp Lipschitz bounds and gradient estimates for fully nonlinear parabolic equations with bounded initial data, via comparison with one-dimensional solutions. This work extends multiple results of Andrews and Clutterbuck for quasilinear equations to fully nonlinear equations.
