Related papers: Optimal control for the conformal Laplacian obstac…
We study wave maps from the circle to a general compact Riemannian manifold. We prove that the global controllability of this geometric equation is characterized precisely by the homotopy class of the data. As a remarkable intermediate…
In this paper we study we study a Dirichlet optimal control prob- lem associated with a linear elliptic equation the coefficients of which we take as controls in the class of integrable functions. The characteristic feature of this control…
A special class of optimal control problems with complementarity constraints on the control functions is studied. It is shown that such problems possess optimal solutions whenever the underlying control space is a first-order Sobolev space.…
We study the optimization of the positive principal eigenvalue of an indefinite weighted problem, associated with the Neumann Laplacian in a box $\Omega\subset\mathbb{R}^N$, which arises in the investigation of the survival threshold in…
Within this chapter, we discuss control in the coefficients of an obstacle problem. Utilizing tools from H-convergence, we show existence of optimal solutions. First order necessary optimality conditions are obtained after deriving…
The paper is concerned with the maximization of Laplace eigenvalues on surfaces of given volume with a Riemannian metric in a fixed conformal class. A significant progress on this problem has been recently achieved by Nadirashvili-Sire and…
We show that in an arbitrarily fixed conformal class on a closed manifold, the upper bound condition of the total scalar curvature is $C^{0}$-closed if its Yamabe constant is nonpositive. Moreover, we show that if a conformal class on a…
This paper is concerned with a constrained stochastic linear-quadratic optimal control problem, in which the terminal state is fixed and the initial state is constrained to lie in a stochastic linear manifold. The controllability of…
This paper is concerned with a linear quadratic (LQ, for short) optimal control problem with fixed terminal states and integral quadratic constraints. A Riccati equation with infinite terminal value is introduced, which is uniquely solvable…
For an embedded conformal hypersurface with boundary, we construct critical order local invariants and their canonically associated differential operators. These are obtained holographically in a construction that uses a singular Yamabe…
In this paper we give bounds for the first eigenvalue of the conformal Laplacian and the Yamabe invariant of a compact Riemannian manifold, by using conditions on the Ricci curvature and the diameter and deduce certain conditions on the…
This paper is devoted to the study of a problem arising from a geometric context, namely the conformal deformation of a Riemannian metric to a scalar flat one having constant mean curvature on the boundary. By means of blow-up analysis…
We consider control-constrained linear-quadratic optimal control problems on evolving surfaces. In order to formulate well-posed problems, we prove existence and uniqueness of weak solutions for the state equation, in the sense of…
In the first part of this thesis, we study the Yamabe problem with singularities, that we can announce as follow: Given a compact Riemannian manifold $(M,g)$, find a constant scalar curvature metric, conformal to $g$, when $g$ has not…
The boundary behavior of the singular Yamabe problem has been extensively studied near sufficiently smooth boundaries, while less is known about the asymptotic behavior of solutions near singular boundaries. In this paper, we study the…
An optimal control problem on finite-dimensional positive cones is stated. Under a critical assumption on the cone, the corresponding Bellman equation is satisfied by a linear function, which can be computed by convex optimization. A…
We consider optimal control problems involving two constraint sets: one comprised of linear ordinary differential equations with the initial and terminal states specified and the other defined by the control variables constrained by simple…
We apply iteration schemes and perturbation methods to provide a complete solution of the boundary Yamabe problem with minimal boundary scenario, or equivalently, the existence of a real, positive, smooth solution of $ -\frac{4(n -1)}{n -…
We study problems of optimal boundary control with systems governed by linear hyperbolic partial differential equations. The objective function is quadratic and given by an integral over the finite time interval $(0,\, T)$ that depends on…
In this paper, we investigate the prescribed scalar curvature problem on a non-compact Riemannian manifold $(M, \langle \, , \, \rangle)$, namely the existence of a conformal deformation of the metric $\langle \, , \, \rangle$ realizing a…