Related papers: On a class of coupled obstacle systems
Intersection types have been originally developed as an extension of simple types, but they can also be used for refining simple types. In this survey we concentrate on the latter option; more precisely, on the use of intersection types for…
We consider hierarchical variational inequality problems, or more generally, variational inequalities defined over the set of zeros of a monotone operator. This framework includes convex optimization over equilibrium constraints and…
In this article we use flatness improvement argument to study the regularity of the free boundary for the biharmonic obstacle problem with zero obstacle. Assuming that the solution is almost one-dimensional, and that the non-coincidence set…
We propose and analyze a new dynamical system with a closed-loop control law in a Hilbert space $\mathcal{H}$, aiming to shed light on the acceleration phenomenon for \textit{monotone inclusion} problems, which unifies a broad class of…
We develop methods to solve general optimal stopping problems with opportunities to stop that arrive randomly. Such problems occur naturally in applications with market frictions. Pivotal to our approach is that our methods operate on…
The paper is concerned with a free boundary problem generated by the biharmonic operator and an obstacle. The main goal is to deduce a fully guaranteed upper bound of the difference between the exact minimizer u and any function…
In this paper, we consider the general problem of obstacle avoidance based on dynamical system. The modulation matrix is developed by introducing orthogonal coordinates, which makes the modulation matrix more reasonable. The new…
This paper deals with the obstacle problem for the infinity Laplacian. The main results are a characterization of the solution through comparison with cones that lie above the obstacle and the sharp $C^{1,1/3}$--regularity at the free…
We establish structural properties of optimal stopping problems under time-consistent dynamic (coherent) risk measures, focusing on value function monotonicity and the existence of control limit (threshold) optimal policies. While such…
In this paper we propose two numerical algorithms to solve a coupled PDE-ODE system which models a slow vehicle (bottleneck) moving on a road together with other cars. The resulting system is fully coupled because the dynamics of the slow…
We propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to…
We propose a semi-discrete numerical scheme and establish well-posedness of a class of parabolic systems. Such systems naturally arise while studying the optimal control of grain boundary motions. The latter is typically described using a…
We present a possible kind of generalization of the notion of ordered pairs of cyclic maps and coupled fixed points and its application in modelling of equilibrium in oligopoly markets. We have obtained sufficient conditions for the…
This paper is devoted to the variational inequality problems. We consider two classes of problems, the first is classical constrained variational inequality and the second is the same problem with functional (inequality type) constraints.…
In this paper we study the continuous dependence with respect to obstacles for obstacle problems with measure data. This is deeply investigated introducing a suitable type of convergence, which gives stability under very general hypotheses.…
We discretize the Lagrange multiplier formulation of the obstacle problem by mixed and stabilized finite element methods. A priori and a posteriori error estimates are derived and numerically verified.
The Maximum Flow Problem with Conflict Constraints is a generalization that adds conflict constraints to a classical optimization problem on networks used to model several real-world applications. In the last few years several approaches,…
In this paper non-transversal intersection of the free and fixed boundary is shown to hold in any dimension for obstacle problems generated by fully nonlinear uniformly elliptic operators. Moreover, $C^1$ regularity results of the free…
We study some regularity issues for solutions of non-autonomous obstacle problems with $(p,q)$-growth. Under suitable assumptions, our analysis covers the main models available in the literature.
In this investigation we revisit the concept of "effective free surfaces" arising in the solution of the time-averaged fluid dynamics equations in the presence of free boundaries. This work is motivated by applications of the optimization…