caa a22 4500 463205987 CHVBK 20180405153126.0 cr unu---uuuuu 170326e20070301xx s 000 0 eng 10.1007/s11228-006-0018-4 doi (NATIONALLICENCE)springer-10.1007/s11228-006-0018-4 Regularity of Solution Maps of Differential Inclusions Under State Constraints [Elektronische Daten] [Piernicola Bettiol, Hélène Frankowska] Consider a differential inclusion under state constraints $$x'(t) \in F(t,x(t)), \; x(t) \in K,$$ where $F$ is an unbounded set-valued map with closed and convex images, which is measurable in $t$ and $k(t)$ -Lipschitz in $x$ (with $k(\cdot)\in L^1$ ) and $K\subset\mathbb{R}^{n}$ is a closed set with smooth boundary. We provide sufficient conditions for the set-valued map $\xi_0 \leadsto {\cal S}^K_{[t_0,T\,]}(\xi_0)$ associating to each initial point $\xi_0 \in K$ the set of all solutions to the above constrained differential inclusion starting at $\xi_0$ to be pseudo-Lipschitz on $K$ . This result is applied to investigate local Lipschitz continuity of the value function for the constrained Bolza problem of optimal control theory. Springer Science+Business Media B.V., 2006 differential inclusions nationallicence state constraints nationallicence pseudo-Lipschitz dependence on initial conditions nationallicence Bettiol Piernicola SISSA/ISAS, 2-4 via Beirut, 34013, Trieste, Italy aut Frankowska Hélène CNRS, CREA, École Polytechnique, 1 Rue Descartes, 75005, Paris, France aut Set-Valued Analysis Kluwer Academic Publishers 15/1(2007-03-01), 21-45 0927-6947 15:1<21 2007 15 11228 https://doi.org/10.1007/s11228-006-0018-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11228-006-0018-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bettiol Piernicola SISSA/ISAS, 2-4 via Beirut, 34013, Trieste, Italy aut NATIONALLICENCE 700 1- Frankowska Hélène CNRS, CREA, École Polytechnique, 1 Rue Descartes, 75005, Paris, France aut NATIONALLICENCE 773 0- Set-Valued Analysis Kluwer Academic Publishers 15/1(2007-03-01), 21-45 0927-6947 15:1<21 2007 15 11228 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer