论文标题
在抽象Wiener空间中的sobolev空间的表征
Characterizations of Sobolev spaces on sublevel sets in abstract Wiener spaces
论文作者
论文摘要
在本文中，我们考虑了一个抽象的Wiener空间$（x，γ，h）$和一个开放子集$ o \ subseteq x $，它满足合适的假设。对于（1，+\ infty）$中的每一个$ p \，我们定义sobolev space $ w_ {0}^{1，p}（o，γ）$作为Lipschitz的封闭函数的关闭，这些功能以$ \ fartial o $ $ $ $ $ $ o $ o $ o o $ o o o o o o o o o o o o o o o o $ o o o $ o o $ o $W_{0}^{1,p}(O,γ)$ can be characterized as the space of functions in $W^{1,p}(O,γ)$ which have null trace at the boundary $\partial O$, or, equivalently, as the space of functions defined on $O$ whose trivial extension belongs to $W^{1,p}(X,γ)$.
In this paper we consider an abstract Wiener space $(X,γ,H)$ and an open subset $O\subseteq X$ which satisfies suitable assumptions. For every $p\in(1,+\infty)$ we define the Sobolev space $W_{0}^{1,p}(O,γ)$ as the closure of Lipschitz continuous functions which support with positive distance from $\partial O$ with respect to the natural Sobolev norm, and we show that under the assumptions on $O$ the space $W_{0}^{1,p}(O,γ)$ can be characterized as the space of functions in $W^{1,p}(O,γ)$ which have null trace at the boundary $\partial O$, or, equivalently, as the space of functions defined on $O$ whose trivial extension belongs to $W^{1,p}(X,γ)$.
