Abstract We prove the validity of the ε - ε β {\varepsilon-\varepsilon^{\beta}} property in the isoperimetric problem with double density, generalising the known properties for the case of single density. As a consequence, we derive regularity for isoperimetric sets.

中文翻译：

---

双密度等周问题中的ε-εβ性质及等周集的正则性

摘要 我们证明了ε - ε β {\varepsilon-\varepsilon^{\beta}} 性质在双密度等周问题中的有效性，推广了单密度情况下的已知性质。因此，我们推导出等周集的规律性。