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.

中文翻译：

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非线性环境中的能量空间、狄利克雷形式和容量

在本文中，我们研究实 Hilbert 空间上的下半连续凸泛函。在文章的第一部分，我们构造了一个 Banach 空间，作为此类泛函的能量空间。在第二部分中，我们研究了 Cipriani 和 Grillo 定义的非线性狄利克雷形式，并表明，正如在双线性情况下众所周知的那样，这种形式的能量空间是一个格子。我们定义了一个容量并引入了与这些形式相关的准连续性的概念，并证明了几个在双线性情况下众所周知的结果。