Hölder norm estimates for elliptic operators on finite and infinite-dimensional spaces
Hölder norm estimates for elliptic operators on finite and infinite-dimensional spaces
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有限维和无限维空间上椭圆算子的霍尔德范数估计
DOI：
10.1090/s0002-9947-05-03638-x
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发表时间：
2005
影响因子：
1.3
通讯作者：
E. Perkins
中科院分区：
文献类型：
--
作者：
S. Athreya;R. Bass;E. Perkins
本文介绍了一种新的证明方法.其中u解方程Δu − λu = f。该方法可应用于R ∞上的Laplacian。当我们用无限维的Ornstein-Uhlenbeck算子或其他椭圆算子代替拉普拉斯算子时，它也允许我们获得类似的估计。这些运营商自然出现在鞅问题所产生的测度值分支扩散和随机偏微分方程。
We introduce a new method for proving the estimate Equation Omitted. Where u solves the equation Δu − λu = f. The method can be applied to the Laplacian on R ∞ . It also allows us to obtain similar estimates when we replace the Laplacian by an infinite-dimensional Ornstein-Uhlenbeck operator or other elliptic operators. These operators arise naturally in martingale problems arising from measure-valued branching diffusions and from stochastic partial differential equations.