论文标题
分数单方面测量理论二阶椭圆算子和随机部分微分方程的应用
Fractional one-sided measure theoretic second-order elliptic operators and applications to stochastic partial differential equations
论文作者
论文摘要
在这项工作中，我们介绍并研究了分数测量的理论椭圆算子，并在圆环上和一个名为W-Brownian运动的新随机过程。我们建立了与上述运营商有关的一些规律性和光谱结果，更确切地说，我们能够为特征值的特征值问题提供急剧的界限。此外，我们展示了与W-Brownian运动相关的Cameron-Martin空间与与上述椭圆运算符相关的Sobolev空间之间的关系。最后给出了在随机部分微分方程上开发的理论的应用。
In this work we introduce and study fractional measure theoretic elliptic operators on the torus and a new stochastic process named W-Brownian motion. We establish some regularity and spectral results related to the operators cited above, more precisely, we were able to provide sharp bounds for the growth rate of eigenvalues to an associated eigenvalue problem. Moreover, we show how the Cameron-Martin space associated to the W-Brownian motion relates to Sobolev spaces connected with the elliptic operators mentioned above. Finally applications of the theory developed on stochastic partial differential equations are given.
