相关论文: Ahlfors-regularity for minimizers of a multiphase …
In the past decade, a combination of unfitted finite elements (or XFEM) with the Nitsche method has become a popular discretization method for elliptic interface problems. This development started with the introduction and analysis of this…
In the Allen-Cahn theory of phase transitions, minimizers partition the domain in subregions, the sets where a minimizer is near to one or to another of the zeros of the potential. These subregions that model the phases are separated by a…
This paper develops and analyses numerical approximation for linear-quadratic optimal control problem governed by elliptic interface equations. We adopt variational discretization concept to discretize optimal control problem, and apply an…
Some optimization problems coming from the Differential Geometry, as for example, the minimal submanifolds problem and the harmonic maps problem are solved here via interior solutions of appropriate multitime optimal control problems.…
Splitting and projection-type algorithms have been applied to many optimization problems due to their simplicity and efficiency, but the application of these algorithms to optimal control is less common. In this paper we utilize the…
In this article we study the second variation of the energy functional associated to the Allen-Cahn equation on closed manifolds. Extending well known analogies between the gradient theory of phase transitions and the theory of minimal…
This paper is devoted to variational problems on the set of probability measures which involve optimal transport between unequal dimensional spaces. In particular, we study the minimization of a functional consisting of the sum of a term…
In materials that undergo martensitic phase transformation, macroscopic loading often leads to the creation and/or rearrangement of elastic domains. This paper considers an example {involving} a single-crystal slab made from two martensite…
We examine the minimization of a quadratic cost functional composed of the output and the final state of abstract infinite-dimensional evolution equations in view of existence of solutions and optimality conditions. While the initial value…
We study the problem of constructing $k$-spectral minimal partitions of domains in $d$ dimensions, where the energy functional to be minimized is a $p$-norm ($1 \le p \le \infty$) of the infimum of the spectrum of a suitable Schr\"odinger…
This paper investigates a space-time interface-fitted approximation of a moving-interface optimal control problem with energy regularization. We reformulate the optimality conditions into a variational problem involving both the state and…
We analyse an energy minimisation problem recently proposed for modelling smectic-A liquid crystals. The optimality conditions give a coupled nonlinear system of partial differential equations, with a second-order equation for the…
Our concern is the computation of optimal shapes in problems involving $\(-\Delta)^{1/2}$. We focus on the energy $J(\Omega)$ associated to the solution $u\_\Omega$ of the basic Dirichlet problem $(-\Delta)^{1/2} u\_\Omega = 1$ in $\Omega$,…
We study the branch of semi-stable and unstable solutions (i.e., those whose Morse index is at most one) of the Dirichlet boundary value problem $-\Delta u=\frac{\lambda f(x)}{(1-u)^2}$ on a bounded domain $\Omega \subset \R^N$, which…
This paper characterizes the solution to a finite horizon min-max optimal control problem where the system is linear and discrete-time with control and state constraints, and the cost quadratic; the disturbance is negatively costed, as in…
Progresses in additive manufacturing technologies allow the realization of finely graded microstructured materials with tunable mechanical properties. This paves the way to a wealth of innovative applications, calling for the combined…
For the Alt-Caffarelli problem, we study free boundary regularity of energy minimizers. In six dimensions, we show that free boundaries are analytic for generic boundary data. In general, we improve previous generic Hausdorff dimensions of…
This article presents an error analysis of the symmetric linear/bilinear partially penalized immersed finite element (PPIFE) methods for interface problems of Helmholtz equations. Under the assumption that the exact solution possesses a…
In this paper we propose a new finite element method for solving elliptic optimal control problems with pointwise state constraints, including the distributed controls and the Dirichlet or Neumann boundary controls. The main idea is to use…
We establish interior regularity and optimal growth estimates for sign-changing minimizers of the $p-$singular or $p-$degenerate quasilinear Alt--Phillips functional throughout the full range of $1<p<\infty$ and of the nonlinearity power…