Related papers: Partial regularity for minimizing constraint maps …

Since the seminal work of Schoen-Uhlenbeck, many authors have studied properties of harmonic maps satisfying Dirichlet boundary conditions. In this article, we instead investigate regularity and symmetry of $\mathbb{S}^2-$valued minimizing…

We introduce a notion of non-local almost minimal boundaries similar to that introduced by Almgren in geometric measure theory. Extending methods developed recently for non-local minimal surfaces we prove that flat non-local almost minimal…

In this paper, we present a comprehensive proof concerning the regularity of critical points for the spline energy functional on Riemannian manifolds, even for the general higher-order case. Although this result is widely acknowledged in…

In this paper an iterative minimization method is proposed to approximate the minimizer to the double-well energy functional arising in the phase-field theory. The method is based on a quadratic functional posed over a nonempty closed…

We study the existence and regularity of energy-minimizing harmonic almost complex structures. We have proved results similar to the theory of harmonic maps, notably the classical results of Schoen-Uhlenbeck and recent advance by…

Compressed sensing involves solving a minimization problem with objective function $\Omega(\boldsymbol{x}) = \|\boldsymbol{x}\|_1$ and linear constraints $\boldsymbol{A} \boldsymbol{x} = \boldsymbol{b}$. Previous work has explored…

We consider volume-constrained minimizers of the fractional perimeter with the addition of a potential energy in the form of a volume inte- gral. Such minimizers are solutions of the prescribed fractional curvature problem. We prove…

We investigate minimizers defined on a bounded domain in $\mathbb{R}^2$ for the Maier--Saupe Q--tensor energy used to characterize nematic liquid crystal configurations. The energy density is singular, as in Ball and Mujamdar's modification…

We provide a simple proof of the radial symmetry of any nonnegative minimizer for a general class of quasi-linear minimization problems.

This paper discusses the regularity of multiple-valued Dirichlet minimizing maps into the sphere. It shows that even at branched point, as long as the normalized energy is small enough, we have the energy decay estimate. Combined with the…

We provide a simple proof of the radial symmetry of any nonnegative minimizer for a general class of quasi-linear minimization problems

In this article, we consider and analyse a small variant of a functional originally introduced in \cite{BLS,LS} to approximate the (geometric) planar Steiner problem. This functional depends on a small parameter $\varepsilon>0$ and…

We obtain existence of minimizers for the $p$-capacity functional defined with respect to a centrally symmetric anisotropy for $1 < p<\infty$, including the case of a crystalline norm in $\mathbb R^N$. The result is obtained by a…

We consider triplets of densities $(u_1,u_2,u_3)$ minimizing the Dirichlet energy \[\sum_{j=1}^3 \int_{\Omega} |\nabla u_j|^2\,dx \] over a bounded domain $\Omega\subset \mathbb{R}^N$, subject to the partial segregation condition: \[…

We establish regularity results for almost-minimizers of a class of variational problems involving both bulk and interface energies. The bulk energy is of Dirichlet type. The surface energy exhibits anisotropic behaviour and is defined by…

We consider maps $T$ solving the optimal transport problem with a cost $c(x-y)$ modeled on the $p$-cost. For H\"older continuous marginals, we prove a $C^{1,\alpha}$-partial regularity result for $T $in the set $\{|T(x)-x|>0\}$.

For a fixed constant $\lambda > 0$ and a bounded Lipschitz domain $\Omega \subset \mathbb{R}^n$ with $n \geq 2$, we establish that almost-minimizers (functions satisfying a sort of variational inequality) of the Alt-Caffarelli type…

We give an alternative proof of the regularity, up to the loose end, of minimizers, resp. critical points of the Mumford-Shah functional when they are sufficiently close to the cracktip, resp. they consist of a single arc terminating at an…

This paper establishes comprehensive stability results for quasi-variational inequalities (QVIs) under monotone perturbations of the governing operator. We prove strong convergence of both minimal and maximal solutions when sequences of…

For a fixed constant $\lambda > 0$ and a bounded Lipschitz domain $\Omega \subset \mathbb{R}^n$ with $n \geq 2$, we establish that almost-minimizers (functions satisfying a sort of variational inequality) of the Alt-Caffarelli type…