Local matching indicators for transport with concave costs

In this note, we introduce a class of indicators that enable to compute efficiently optimal transport plans associated to arbitrary distributions of $N$ demands and $N$ supplies in $\mathbf{R}$ in the case where the cost function is concave. The computational cost of these indicators is small and independent of $N$. A hierarchical use of them enables to obtain an efficient algorithm

A note on the difference schemes for hyperbolic-elliptic equations

The nonlocal boundary value problem for hyperbolic-elliptic equation d2u(t)/dt2+Au(t)=f(t), (0≤t≤1), −d2u(t)/dt2+Au(t)=g(t), (−1≤t≤0), u(0)=ϕ, u(1)=u(−1) in a Hilbert space H is considered. The second order of accuracy difference schemes for approximate solutions of this boundary value problem are presented. The stability estimates for the solution of these difference schemes are established

Optimal Regularity for a Class of Singular Abstract Parabolic Equations

A general class of singular abstract Cauchy problems is considered which naturally arises in applications to certain Free Boundary Problems. Existence of an associated evolution operator characterizing its solutions is established and is subsequently used to derive optimal regularity results. The latter are well known to be important basic tools needed to deal with corresponding nonlinear Cauchy Problems such as those associated to Free Boundary Problems