State dependent nonconvex sweeping processes in smooth Banach spaces
In this paper, the authors prove the existence of the solution for a state dependent nonconvex sweeping process (SDNSP), represented by the following multivalued differential equation \[ -\frac{d}{dt} J(u(t))\in N^{C}(t,u(t);u(t))\;\text{ for a.e. } t\in [0,T], \] where \(N^{C}\) stands for the Clarke normal cone. The context is that of a \(2\)-uniformly smooth and \(q\)-uniformly convex Banach space. A perturbed state dependent nonconvex sweeping process is also considered. The results extend recent existing results from the setting of Hilbert spaces to the setting of Banach spaces.
\(V\)-uniformly generalized prox-regularity
scientific article; zbMATH DE number 7348213