Blow-up analysis of stationary two-valued functions

Abstract

Abstract. We consider two-valued real functions of two variables which are stationary with respect to both domain and range transformations. We prove their local Lipschitz continuity and use it to establish strong convergence in W1,2 to their unique blow-up at any point. The main theorem of this paper states that the branch set of any such function consists of finitely many real analytic curves meeting at nod points with equal angles. We also provide an example showing that stationarity with respect to domain transformations only does not imply continuity.