Related papers: A minimisation problem in ${\mathrm{L}}^\infty$ wi…

We consider a parabolic optimal control problem with an initial measure control. The cost functional consists of a tracking term corresponding to the observation of the state at final time. Instead of a regularization term in the cost…

Shape optimization models with one or more shapes are considered in this chapter. Of particular interest for applications are problems in which where a so-called shape functional is constrained by a partial differential equation (PDE)…

Motivated by many applications in complex domains with boundaries exposed to large topological changes or deformations, fictitious domain methods regard the actual domain of interest as being embedded in a fixed Cartesian background. This…

This paper addresses the estimation of uncertain distributed diffusion coefficients in elliptic systems based on noisy measurements of the model output. We formulate the parameter identification problem as an infinite dimensional…

We introduce an unfitted finite element method with Lagrange-multipliers to study an Eulerian time stepping scheme for moving domain problems applied to a model problem where the domain motion is implicit to the problem. We consider a…

We would like to study the solution stability of a parametric control problem governed by semilinear elliptic equations with a mixed state-control constraint, where the cost function is nonconvex and the admissible set is unbounded. The…

This work studies how the choice of the representation for parametric, spatially distributed inputs to elliptic partial differential equations (PDEs) affects the efficiency of a polynomial surrogate, based on Taylor expansion, for the…

Consider the supremal functional \[ \tag{1} \label{1} E_\infty(u,A) \,:=\, \|L(\cdot,u,D u)\|_{L^\infty(A)},\quad A\subseteq \Omega, \] applied to $W^{1,\infty}$ maps $u:\Omega\subseteq \mathbb{R}\longrightarrow \mathbb{R}^N$, $N\geq 1$.…

For a Hamiltonian $K \in C^2(\mathbb{R}^{N \times n})$ and a map $u:\Omega \subseteq \mathbb{R}^n \longrightarrow \mathbb{R}^N$, we consider the supremal functional \[ \label{1} \tag{1} E_\infty (u,\Omega) \ :=\…

We consider the following class of online optimization problems with functional constraints. Assume, that a finite set of convex Lipschitz-continuous non-smooth functionals are given on a closed set of $n$-dimensional vector space. The…

The aim of this work is to study, from an intrinsic and geometric point of view, second-order constrained variational problems on Lie algebroids, that is, optimization problems defined by a cost functional which depends on higher-order…

Overdetermined systems of first kind integral equations appear in many applications. When the right-hand side is discretized, the resulting finite-data problem is ill-posed and admits infinitely many solutions. We propose a numerical method…

We consider an elliptic partial differential equation in non-divergence form with a random diffusion matrix and random forcing term. To address this, we propose a mixed-type continuous finite element discretization in the physical domain,…

We prove an existence and uniqueness result for Neumann boundary problem of a parabolic partial differential equation (PDE for short) with a singular nonlinear divergence term which can only be understood in a weak sense. A probabilistic…

This paper aims to study the convergence of adaptive finite element method for control constrained elliptic optimal control problems under $L^2$-norm. We prove the contraction property and quasi-optimal complexity for the $L^2$-norm errors…

We consider the problem of minimizing variational integrals defined on \cc{nonlinear} Sobolev spaces of competitors taking values into the sphere. The main novelty is that the underlying energy features a non-uniformly elliptic integrand…

In this paper we consider a mass optimization problem in the case of scalar state function, where instead of imposing a constraint on the total mass of the competitors, we penalize the classical compliance by a convex functional defined on…

An optimal control problem subject to an elliptic obstacle problem is studied. We obtain a numerical approximation of this problem by discretising the PDE obtained via a Moreau--Yosida type penalisation. For the resulting discrete control…

In the contest of optimal control problems, regularity results for optima are known when addressing fiber-strictly convex Lagrangian. For infinite time horizons, or for settings with infinite dimensional dynamics, the equivalence between…

For numerical approximation the reformulation of a PDE as a residual minimisation problem has the advantages that the resulting linear system is symmetric positive definite, and that the norm of the residual provides an a posteriori error…