论文标题
在非线性环境中
Energy Spaces, Dirichlet Forms and Capacities in a Nonlinear Setting
论文作者
论文摘要
在本文中，我们研究了实际希尔伯特空间上的较低半连续的凸功能。在本文的第一部分中，我们构建了一个Banach空间，该空间是此类功能的能量空间。在第二部分中，我们研究了由Cipriani和Grillo定义的非线性Dirichlet形式，并显示了在双线性情况下众所周知的，这种形式的能量空间是晶格。我们定义了一个能力，并引入了与这些形式相关的概念的准持续性，并证明了几个结果，这在双线性情况下是众所周知的。
In this article we study lower semicontinuous, convex functionals on real Hilbert spaces. In the first part of the article we construct a Banach space that serves as the energy space for such functionals. In the second part we study nonlinear Dirichlet forms, as defined by Cipriani and Grillo, and show, as it is well known in the bilinear case, that the energy space of such forms is a lattice. We define a capacity and introduce the notion quasicontinuity associated with these forms and prove several results, which are well known in the bilinear case.
