论文标题
$ l_p $ - 在$ \ mathbb {r}^2 $中的角域上随机热方程的理论
An $L_p$-theory for the stochastic heat equation on angular domains in $\mathbb{R}^2$ with mixed weights
论文作者
论文摘要
我们为在$ \ mathbb {r}^2 $中的角域上的随机热方程式建立了一个精致的$ l_p $ estimate（$ p \ geq 2 $），基于$ \ mathbb {r}^2 $，基于两者的混合权重，即边界的距离和到达顶点的距离。这样，我们可以捕获解决方案奇点的两个原因：一方面噪声和边界条件的不兼容以及边界奇点（这里是顶点）的影响。还建立了高级$ L_P $ -SOBOLOLEV的规律性。
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.
