We consider the nonlocal Cahn-Hilliard equation with singular potential and degenerate mobility in a bounded domain $\mathrm{\Omega }\subset {\mathbb{R}}^d$, $d\le 3$. We first prove the existence of maximal strong solutions in weighted (in time) $L^p$ spaces. Then we establish further regularity properties of the solution through maximal regularity theory. Finally, we revisit the separation property in an appendix.

中文翻译：

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具有奇异势和简并迁移率的非局部Cahn-Hilliard方程的正则结果

我们考虑具有奇异势的非局部Cahn-Hilliard方程和有界域中的简并迁移率 $\mathrm{\Omega }\subset {\mathbb{[R}}^d$， $d\le 3$。我们首先证明加权（时间上）最大强解的存在${\mathrm{大号}}^p$空格。然后，通过最大正则性理论建立解的进一步正则性。最后，我们在附录中重新介绍了分离属性。