论文标题
关于非局部抛物线方程的扩展问题中的太空分析性
On the space-like analyticity in the extension problem for nonlocal parabolic equations
论文作者
论文摘要
在本说明中，我们给出一个基本证明，证明了解决方案的太空真实分析性，即对$（\ partial_t -div_x（b（x）\ nabla_x）类型的分数抛物线运算符的研究，这是一个退化进化问题。我们的主要兴趣是所谓的\ emph {扩展变量}。我们表明，即使在如此变量中的弱解决方案实际上在空间变量的总体中是实现的。作为此结果的应用，我们证明了上述类型的非局部抛物线运算符的弱唯一延续性属性，其中$ b（x）$是带有实用分析条目的均匀椭圆形矩阵值。
In this note we give an elementary proof of the space-like real analyticity of solutions to a degenerate evolution problem that arises in the study of fractional parabolic operators of the type $(\partial_t - div_x(B(x)\nabla_x))^s$, $0<s<1$. Our primary interest is in the so-called \emph{extension variable}. We show that weak solutions that are even in such variable, are in fact real-analytic in the totality of the space variables. As an application of this result we prove the weak unique continuation property for nonlocal parabolic operators of the type above, where $B(x)$ is a uniformly elliptic matrix-valued function with real-analytic entries.
