A Lipschitz domain is an open connected subset of Euclidean space whose boundary is locally the graph of a Lipschitz continuous function after rotating and translating coordinates. Locally the domain lies on one side of that graph. This permits corners but excludes boundary cusps that cannot be represented with a finite Lipschitz constant. Bounded Lipschitz domains are a standard setting for Sobolev spaces and the Poincaré inequality for total variation.
