论文标题
索博尔（Sobolev
Sobolev space of functions valued in a monotone Banach family
论文作者
论文摘要
我们将Mertrical方法应用于Sobolev空间，该空间在各种演化PDE中出现。这些空间的功能是在一个间隔中定义的，并在Banach空间家族中取值。在这种情况下，我们适应了牛顿空间的定义。对于单调家族，我们显示了弱衍生物的存在，获得标准Sobolev空间的同构，并提供一些标量特征。
We apply the metrical approach to Sobolev spaces, which arise in various evolution PDEs. Functions from those spaces are defined on an interval and take values in a family of Banach spaces. In this case we adapt the definition of Newtonian spaces. For a monotone family, we show the existence of weak derivative, obtain an isomorphism to the standard Sobolev space, and provide some scalar characteristics.
