论文标题
Lipschitz的密度在能量中起作用
Density of Lipschitz functions in Energy
论文作者
论文摘要
在本文中，我们表明Lipschitz能量的密度在Sobolev空间中起作用$ n^{1，p}（x）$在[1，\ infty）$ in [1，\ infty）$ in [1，\ infty）$中均保留，每当$ x $完整且可分离时，并且该措施是ra子和有限的球。强调，允许$ p = 1 $。我们还为未来的工作提出了一些推论并提出问题。 证明是直接的，不涉及先前工作的通常的流动技术。它还产生了一种新的近似技术，该技术尚未出现在先前的工作中。所有这一切都值得注意的是，我们不使用任何形式的庞加莱不平等或加倍假设。这些技术是灵活的，并提出了有关该主题的各种现有文献的统一。
In this paper, we show that the density in energy of Lipschitz functions in a Sobolev space $N^{1,p}(X)$ holds for all $p\in [1,\infty)$ whenever the space $X$ is complete and separable and the measure is Radon and finite on balls. Emphatically, $p=1$ is allowed. We also give a few corollaries and pose questions for future work. The proof is direct and does not involve the usual flow techniques from prior work. It also yields a new approximation technique, which has not appeared in prior work. Notable with all of this is that we do not use any form of Poincaré inequality or doubling assumption. The techniques are flexible and suggest a unification of a variety of existing literature on the topic.
