Lp Hardy inequality on C1,γ domains

We consider the L p Hardy inequality involving the distance to the boundary of a domain in the n-dimensional Euclidean space with nonempty compact boundary. We extend the validity of known existence and non-existence results, as well as the appropriate tight decay estimates for the corresponding minimizers, from the case of domains of class C2 to the case of domains of class C1,γ with γ 2 (0, 1]. We consider both bounded and exterior domains. The upper and lower estimates for the minimizers in the case of exterior domains and the corresponding related non-existence result seem to be new even for C2-domains.