Lipschitz continuity of copulas w.r.t. LpLp-norms

In the framework of the stability analysis of real functions, the Lipschitz continuity of copulas w.r.t. LpLp-norms is investigated. Emphasis is put on 1-Lipschitz continuity, as it is the strongest type possible for copulas. After illustrating how to identify 1-Lipschitz copulas w.r.t. some LpLp-norm, the preservation of this 1-Lipschitz continuity by certain construction methods, such as ordinal sums and convex sums, is demonstrated. Special attention is given to three important classes of copulas, namely Archimedean copulas, extreme value copulas and Archimax copulas.