In this paper we study a double phase problem with an irregular obstacle. The energy functional under consideration is characterized by the fact that both ellipticity and growth switch between a type of polynomial and a type of logarithm, which can be regarded as a borderline case of the double phase functional with $(p,q)$‐growth. We obtain an optimal global Calderón–Zygmund type estimate for the obstacle problem with double phase in the borderline case.

中文翻译：

---

临界情况下双相非线性障碍物问题

在本文中，我们研究具有不规则障碍的双相问题。所考虑的能量泛函的特征在于，椭圆率和增长都在多项式和对数之间切换，这可以看作是双相泛函的临界情况。$（p，q）$增长。对于边界情况下具有双相的障碍问题，我们获得了最优的全局Calderón–Zygmund类型估计。