Related papers: A sharp quantitative stability result near infinit…

This study aims to construct a stable, high-order compact finite difference method for solving Sobolev-type equations with Dirichlet boundary conditions in one-space dimension. Approximation of higher-order mixed derivatives in some…

This paper concerns piecewise-smooth maps on $\mathbb{R}^d$ that are continuous but not differentiable on switching manifolds (where the functional form of the map changes). The stability of fixed points on switching manifolds is…

This paper is concerned with a shape optimization problem governed by a non-smooth PDE, i.e., the nonlinearity in the state equation is not necessarily differentiable. We follow the functional variational approach of [40] where the set of…

We present an existence and stability theory for gravity-capillary solitary waves with constant vorticity on the surface of a body of water of finite depth. Exploiting a rotational version of the classical variational principle, we prove…

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…

For a given family of smooth closed curves $\gamma^1,...,\gamma^\alpha\subset\mathbb{R}^3$ we consider the problem of finding an elastic \emph{connected} compact surface $M$ with boundary $\gamma=\gamma^1\cup...\cup\gamma^\alpha$. This is…

As the energy of any map $v$ from $S^2$ to $S^2$ is at least $4\pi \vert deg(v)\vert$ with equality if and only if $v$ is a rational map one might ask whether maps with small energy defect $\delta_v=E(v)-4\pi \vert deg(v)\vert$ are…

Minimizers in the least gradient problem with discontinuous boundary data need not be unique. However, all of them have a similar structure of level sets. Here, we give a full characterization of the set of minimizers in terms of any one of…

We study zero-temperature stability of topological phases of matter under weak time-independent perturbations. Our results apply to quantum spin Hamiltonians that can be written as a sum of geometrically local commuting projectors on a…

We prove the sharp quantitative stability for a wide class of weighted isoperimetric inequalities. More precisely, we consider isoperimetric inequalities in convex cones with homogeneous weights. Inspired by the proof of such isoperimetric…

We develop a comprehensive study on sharp potential type Riemannian Sobolev inequalities of order 2 by means of a local geometric Sobolev inequality of same kind and suitable De Giorgi-Nash-Moser estimates. In particular we discuss…

We prove a compactness and semicontinuity result that applies to minimisation problems in nonhomogeneous linear elasticity under Dirichlet boundary conditions. This generalises a previous compactness theorem that we proved and employed to…

Let $\Omega$ be a smooth bounded axisymmetric set in $\R^3$. In this paper we investigate the existence of minimizers of the so-called neo-Hookean energy among a class of axisymmetric maps. Due to the appearance of a critical exponent in…

We propose a new class of finite element approximations to ideal compressible magnetohydrodynamic equations in smooth regime. Following variational approximations developed for fluid models in the last decade, our discretizations are built…

Based on a quantitative version of the inverse function theorem and an appropriate saddle-point formulation we derive a quasi-optimal error estimate for the finite element approximation of harmonic maps into spheres with a nodal…

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…

Using purely variational methods, we prove local and global higher integrability results for upper gradients of quasiminimizers of a $(p,q)$-Dirichlet integral with fixed boundary data, assuming it belongs to a slightly better Newtonian…

We consider the Dirichlet problem for stationary biharmonic maps $u$ from a bounded, smooth domain $\Omega\subset\mathbb R^n$ ($n\ge 5$) to a compact, smooth Riemannian manifold $N\subset\mathbb R^l$ without boundary. For any smooth…

We consider the numerical computation of a variational problem that arises from materials science. The target functional is a type of elastic energy that is influenced by obstacles and adhesion. Owing to its strong nonlinearity and…

We prove that for each positive integer $N$ the set of smooth, zero degree maps $\psi\colon\mathbb{S}^2\to \mathbb{S}^2$ which have the following three properties: (1) there is a unique minimizing harmonic map $u\colon \mathbb{B}^3\to…