We consider a general class of singular control problems with state constraints. Budhiraja and Ross [Ann. Appl. Probab., 16 (2006), pp. 2235--2255] established the existence optimal controls for relaxed version this by using so-called time-stretching method J1-topology. show that weak-M1 topology is better suited establishing existence, since it allows to bypass time-transformations, without an...

Sufficient conditions ensuring weak lower semi-continuity of the optimal value function are presented. To this end, refined inner semi-continuity properties of set-valued maps are introduced which meet the needs of the weak topology in Banach spaces. The results are applied to prove the existence of solutions in various worst-case robust optimal control problems governed by semilinear elliptic ...

The primary object of this paper is to prove the conjecture of [HL08a] explaining how to recover the weak dimension of a ring from its derived category. In the process, we develop a theory of weak dimension, which we call ghost dimension, for the generalized rings, known as ring spectra, that arise in algebraic topology.

Abstract We show the continuous dependence of solutions linear nonautonomous second-order parabolic partial differential equations (PDEs) with bounded delay on coefficients and delay. The assumptions are very weak: only convergence in weak-* topology is required. results important applications theory Lyapunov exponents to investigation PDEs