Lipschitz continuity of polyhedral Skorokhod maps
Summary: We show that a special stability condition of the associated system of oblique projections (the so-called \(\ell\)-paracontractivity) guarantees that the corresponding polyhedral Skorokhod problem in a Hilbert space \(X\) is solvable in the space of absolutely continuous functions with values in \(X\). If, moreover, the oblique projections are transversal, the solution exists and is unique for each continuous input and the Skorokhod map is Lipschitz continuous in both spaces \(C([0,T];X)\) and \(W^{1,1} (0,T;X)\). Also, an explicit upper bound for the Lipschitz constant is derived.
polyhedral Skorokhod problem in Hilbert space
scientific article; zbMATH DE number 1747392