Title: An integrable bound for semilinear rough partial differential equations with unbounded diffusion coefficients Show Chinese title

Title: 半线性粗糙偏微分方程的可积界与无界扩散系数

Abstract: This work develops moment bounds for the controlled rough path norm of the solution of semilinear rough partial differential equations.~The novel aspects are two-fold: first we consider rough paths of low time regularity $\gamma\in(1/4,1/2)$ and second treat unbounded diffusion coefficients. To this aim we introduce a suitable notion of a controlled rough path according to a monotone scale of Banach spaces and innovative control functions. Show Chinese abstract

Abstract: 这项工作为半线性粗糙偏微分方程解的受控粗糙路径范数建立了矩界。其创新之处有两个方面：首先我们考虑了低时间正则性的粗糙路径$\gamma\in(1/4,1/2)$，其次处理了无界扩散系数。为此，我们根据一个单调的巴拿赫空间尺度和创新的控制函数引入了一个合适的受控粗糙路径的概念。