Related papers: Unstable free boundary problems in optimal control…
We consider both discrete and continuous control problems constrained by a fixed budget of some resource, which may be renewed upon entering a preferred subset of the state space. In the discrete case, we consider both deterministic and…
In this paper, we derive a bang-bang property of a kind of time optimal control problem for some semilinear heat equation on bounded $C^2$ domains (of the Euclidean space), with homogeneous Dirichlet boundary condition and controls…
We consider one-dimensional parabolic free boundary value problem with a nonlocal (integro-differential) condition on the free boundary. Results on $C^m$-regularity of the free boundary are obtained. In particular, a necessary and…
In this paper, we study a boundary control problem associated to the stationary Rayleigh-B\'enard-Marangoni (RBM) system in presence of controls for the velocity and the temperature on parts of the boundary. We analyze the existence,…
Building on the free-probability stochastic control framework introduced in arXiv:2502.17329, we connect optimal control problems for $n \times n$ random matrix ensembles with their infinite-dimensional, free-probability analogues. Under…
We prove the -- to the best knowledge of the authors -- first result on the fine asymptotic behavior of the regular part of the free boundary of the obstacle problem close to singularities. The result is motivated by our recent partial…
We consider the control problem of the stochastic Navier-Stokes equations in multidimensional domains introduced in \cite{ocpc} restricted to noise terms defined by Q-Wiener processes. Using a stochastic maximum principle, we derive a…
Motivated by the applications, a class of optimal control problems is investigated, where the goal is to influence the behavior of a given population through another controlled one interacting with the first. Diffusive terms accounting for…
In this work, we consider optimality conditions of an optimal control problem governed by an obstacle problem. Here, we focus on introducing a, matrix valued, control variable as the coefficients of the obstacle problem. As it is well…
We propose a general framework for studying optimal impulse control problem in the presence of uncertainty on the parameters. Given a prior on the distribution of the unknown parameters, we explain how it should evolve according to the…
We study the free boundary of solutions to the parabolic obstacle problem with fully nonlinear diffusion. We show that the free boundary splits into a regular and a singular part: near regular points the free boundary is $C^\infty$ in space…
In this paper, we consider a class of optimal control problems governed by 1D parabolic state-systems of KWC types with dynamic boundary conditions. The state-systems are based on a phase-field model of grain boundary motion, proposed in…
We will show optimal regularity for minimizers of the Signorini problem for the Lame system. In particular if $\u=(u^1,u^2,u^3)\in W^{1,2}(B_1^+:\R^3)$ minimizes $$ J(\u)=\int_{B_1^+}|\nabla \u+\nabla^\bot \u|^2+\lambda\div(\u)^2 $$ in the…
We consider optimal control problems where the state equation is an elliptic PDE of a Schr\"odinger type, governed by the Laplace operator $-\Delta$ with the addition of a potential V, and the control is the potential V itself, that may…
We consider fully nonlinear obstacle-type problems of the form \begin{equation*} \begin{cases} F(D^{2}u,x)=f(x) & \text{a.e. in}B_{1}\cap\Omega,|D^{2}u|\le K & \text{a.e. in}B_{1}\backslash\Omega, \end{cases} \end{equation*} where $\Omega$…
In this paper, we study a time optimal internal control problem governed by the heat equation in $\Omega\times [0,\infty)$. In the problem, the target set $S$ is nonempty in $L^2(\Omega)$, the control set $U$ is closed, bounded and nonempty…
We investigate symmetry reduction of optimal control problems for left-invariant control systems on Lie groups, with partial symmetry breaking cost functions. Our approach emphasizes the role of variational principles and considers a…
In this work, a boundary control problem for the following generalized Burgers-Huxley (GBH) equation: $$u_t=\nu u_{xx}-\alpha u^{\delta}u_x+\beta u(1-u^{\delta})(u^{\delta}-\gamma), $$ where $\nu,\alpha,\beta>0,$ $1\leq\delta<\infty$,…
This article concerns a class of time-optimal state constrained control problems with dynamics defined by an ordinary differential equation involving a three-dimensional steady flow vector field. The problem is solved via an indirect method…
The theory of boundary regularity for $p$-harmonic functions is extended to unbounded open sets in complete metric spaces with a doubling measure supporting a $p$-Poincar\'e inequality, $1<p<\infty$. The barrier classification of regular…