$\mathbb{R}^2$中角域上随机heat equation的混合权$L_p$ -理论
An $L_p$-theory for the stochastic heat equation on angular domains in $\mathbb{R}^2$ with mixed weights
摘要：
在$\mathbb{R}^2$中，我们建立了角域上的随机热方程的一个改进的$L_p$ -估计（$p\geq 2$），该估计具有基于到边界的距离和到顶点的距离的混合权重。通过这种方式，我们可以捕获解的奇异性的两个原因：一方面是噪声和边界条件的不相容性，另一方面是边界奇异性（这里是顶点）的影响。建立了混合权的高阶$L_p$ -Sobolev正则性.
英文摘要：
We establish a refined $L_p$-estimate ($p\geq 2$) for the stochastic heat equation on angular domains in $\mathbb{R}^2$ with mixed weights based on both, the distance to the boundary and the distance to the vertex. This way we can capture both causes for singularities of the solution: the incompatibility of noise and boundary condition on the one hand and the influence of boundary singularities (here, the vertex) on the other hand. Higher order $L_p$-Sobolev regularity with mixed weights is also established.
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