The EMS Publishing House is now EMS Press and has its new home at

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen

Full-Text PDF (315 KB) | Metadata | Table of Contents | ZAA summary
Volume 20, Issue 4, 2001, pp. 817–844
DOI: 10.4171/ZAA/1047

Published online: 2001-12-31

Lipschitz Continuity of Polyhedral Skorokhod Maps

Pavel Krejcí[1] and A.A. Vladimirov[2]

(1) Academy of Sciences, Praha, Czech Republic
(2) Institute for Information Transmission Problems, Moscow, Russian Federation

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.

Keywords: Polyhedral Skorokhod problem, oblique reflections, Lipschitz continuity

Krejcí Pavel, Vladimirov A.A.: Lipschitz Continuity of Polyhedral Skorokhod Maps. Z. Anal. Anwend. 20 (2001), 817-844. doi: 10.4171/ZAA/1047