论文标题
奇异的HJB方程，并在真实线上应用于KPZ
Singular HJB equations with applications to KPZ on the real line
论文作者
论文摘要
本文致力于研究具有分布值的系数的汉密尔顿 - 雅各比 - 贝尔曼方程，该方程在经典意义上并不明确，并且应使用\ cite {gip15}中引入的paraconollolled分布方法来理解。通过对加权Hölder空间和Zvonkin的转换的新表征，我们证明了一些新的先验估计，因此建立了单数HJB方程的全球范围良好。作为应用程序，在多项式加权Hölder空间中的实际线路上的KPZ方程的全局适合性是无需使用Cole-Hopf的转换而获得的。特别是，我们解决了在\ cite [dempress 1.1] {pr18}中提出的猜想。
This paper is devoted to studying the Hamilton-Jacobi-Bellman equations with distribution-valued coefficients, which is not well-defined in the classical sense and shall be understood by using paracontrolled distribution method introduced in \cite{GIP15}. By a new characterization of weighted Hölder space and Zvonkin's transformation we prove some new a priori estimates, and therefore, establish the global well-posedness for singular HJB equations. As an application, the global well-posedness for KPZ equations on the real line in polynomial weighted Hölder spaces is obtained without using Cole-Hopf's transformation. In particular, we solve the conjecture posed in \cite[Remark 1.1]{PR18}.
