Related papers: Asymptotics of an optimal compliance-location prob…
We consider minimization problems in the calculus of variations set in a sequence of domains the size of which tends to infinity in certain directions and such that the data only depend on the coordinates in the directions that remain…
Given the probability measure $\nu$ over the given region $\Omega\subset \R^n$, we consider the optimal location of a set $\Sigma$ composed by $n$ points $\Om$ in order to minimize the average distance $\Sigma\mapsto \int_\Om…
We consider the problem of optimally locating a given number $k$ of points in ${\mathbb R}^n$ for an integral cost function which takes into account two measures $\varphi^+$ and $\varphi^-$. The points represent for example new industrial…
We construct an asymptotic approximation to the solution of a transmission problem for a body containing a region occupied by many small inclusions. The cluster of inclusions is characterised by two small parameters that determine the…
We prove an asymptotic crystallization result in two dimensions for a class of nonlocal particle systems. To be precise, we consider the best approximation with respect to the 2-Wasserstein metric of a given absolutely continuous…
In the standard formulation of the occupancy problem one considers the distribution of r balls in n cells, with each ball assigned independently to a given cell with probability 1/n. Although closed form expressions can be given for the…
We consider the minimization of integral functionals in one dimension and their approximation by $r$-adaptive finite elements. Including the grid of the FEM approximation as a variable in the minimization, we are able to show that the…
In this paper, we consider asymptotics of the optimal value and the optimal solutions of parametric minimax estimation problems. Specifically, we consider estimators of the optimal value and the optimal solutions in a sample minimax problem…
Large optimal transport problems can be approached via domain decomposition, i.e. by iteratively solving small partial problems independently and in parallel. Convergence to the global minimizers under suitable assumptions has been shown in…
The Pompeiu problem is considered as shape optimization problem. We show stability of the ball which is the minimum point of related domain functional. The proof is based on shape derivative method. Stability of the ball for general domain…
Topology optimization is concerned with the identification of optimal shapes of deformable bodies with respect to given target functionals. The focus of this paper is on a topology optimization problem for a time-evolving elastoplastic…
We generalize the shape optimization problem for the existence of stable equilibrium configurations of nematic and cholesteric liquid crystal drops surrounded by an isotropic solution to include a broader family of admissible domains with…
We study optimal design problems where the design corresponds to a coefficient in the principal part of the state equation. The state equation, in addition, is parameter dependent, and we allow it to change type in the limit of this…
In this paper we study the following problems: given a finite number of nonempty closed subsets of a normed space, find a ball with the smallest radius that encloses all of the sets, and find a ball with the smallest radius that intersects…
We prove some regularity results for a connected set S in the planar domain O, which minimizes the compliance of its complement O\S, plus its length. This problem, interpreted as to find the best location for attaching a membrane subject to…
We investigate a fixed domain approach in shape optimization, using a regularization of the Heaviside function both in the cost functional and in the state system. We consider the compliance minimization problem in linear elasticity, a well…
Determination of \emph{optimal} arrangements of $N$ particles on a sphere is a well-known problem in physics. A famous example of such is the Thomson problem of finding equilibrium configurations of electrical charges on a sphere. More…
We consider the shape optimization problem which consists in placing a given mass $m$ of elastic material in a design region so that the compliance is minimal. Having in mind optimal light structures, our purpose is to show that the problem…
We present filling as a type of spatial subdivision problem similar to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most interior volume. In…
In general, standard necessary optimality conditions cannot be formulated in a straightforward manner for semi-smooth shape optimization problems. In this paper, we consider shape optimization problems constrained by variational…