This paper deals with the Lipschitz regularity of minimizers for a class of variational obstacle problems with possible occurrence of the Lavrentiev phenomenon. In order to overcome this problem, the availment of the notions of relaxed functional and Lavrentiev gap is needed. The main tool used here is a crucial Lemma which reveals to be needed because it allows us to move from the variational obstacle problem to the relaxed-functional-related one. This is fundamental in order to find the solutions’ regularity that we intended to study. We assume the same Sobolev regularity both for the gradient of the obstacle and for the coefficients.

中文翻译：

---

没有结构条件的障碍物问题的规律性

本文讨论了可能发生Lavrentiev现象的一类变分障碍问题的极小化器的Lipschitz正则性。为了克服这个问题，需要使用松弛的功能和拉夫伦蒂夫差距的概念。这里使用的主要工具是关键的引理，它表明是必需的，因为它使我们能够从变化障碍问题转移到与功能松弛相关的问题。这是找到我们打算研究的解决方案规律性的基础。对于障碍物的坡度和系数，我们假设相同的Sobolev正则性。