Gradient estimates for pp-Laplacian equation in composite Reifenberg domains

We obtain a local gradient estimate for weak solutions of pp-Laplacian type equation in a non-smooth domain composed of a finite number of disjoint subdomains with (δ0,R)(δ0,R)-Reifenberg flat boundaries. This kind of domain was called (δ0,R)(δ0,R) composite-Reifenberg domain, which allows certain subdomain to exist with highly non-smooth boundaries worse than Reifenberg domain. Our results improve the known results for such equations.