Related papers: Hyperelastic deformations and total combined energ…

We consider the existence and uniqueness of a minimizer of the extremal problem for weighted combined energy between two concentric annuli and obtain that the extremal mapping is a certain radial mapping. Meanwhile, this in turn implies a…

Let $\mathbb{A}$ and $\mathbb{A_{*}}$ be two non-degenerate spherical annuli in $\mathbb{R}^{n}$ equipped with the Euclidean metric and the weighted metric $|y|^{1-n}$, respectively. Let $\mathcal{F}(\mathbb{A},\mathbb{A_{*}})$ denote the…

The main aim of this paper is to extend one of the main results of Iwaniec and Onninen (Arch. Ration. Mech. Anal., 194: 927-986, 2009). We prove that, the so called total energy functional defined on the class of radial streachings between…

Let $\mathbb{A}$ and $\mathbb{B}$ be circular annuli in the complex plane and consider the Dirichlet energy integral of $j-$degree mappings between $\mathbb{A}$ and $\mathbb{B}$. Then we minimize this energy integral. The minimizer is a…

We extend the main results obtained by Iwaniec and Onninen in Memoirs of the AMS (2012). In the paper it is solved the minimization problem of $(\rho,n)$ energy of Sobolev homeomorphisms between two concentric annuli in the Euclidean space…

Let $A$ and $A'$ be two circular annuli and let $\rho$ be a radial metric defined in the annulus $A'$. Consider the class $\mathcal H_\rho$ of $\rho-$harmonic mappings between $A$ and $A'$. It is proved recently by Iwaniec, Kovalev and…

We study compressible and incompressible nonlinear elasticity variational problems in a general context. Our main result gives a sufficient condition for an equilibrium to be a global energy minimizer, in terms of convexity properties of…

We investigate equilibria of charged deformable materials via the minimization of an electroelastic energy. This features the coupling of elastic response and electrostatics by means of a capacitary term, which is naturally defined in…

Given two annuli $\mathbf{A}(r,R)$ and $\mathbf{A}(r_\ast, R_\ast)$, in $\mathbf{R}^3$ equipped with the Euclidean metric and the weighted metric $|y|^{-2}$ respectively, we minimize the Dirichlet integral, i.e. the functional…

It has been found in numerical experiments that when one removes a sector from an elastic sheet and glues the edges of the sector back together, the resulting configuration is radially symmetric and nearly conical. We make a rigorous…

We propose a model for nonlinearly elastic membranes undergoing finite deformations while confined to a regular frictionless surface in $\mathbb{R}^3$. This is a physically correct model of the analogy sometimes given to motivate harmonic…

Let $A_1$ and $A_2$ be two circular annuli and let $\rho$ be a radial metric defined in the annuli $A_2$. We study the existence and uniqueness of the extremal problem for weighted combined energy between $A_1$ and $A_2$, and obtain that…

In this note we prove that any $W^{1,2}$ mapping $u$ in the plane that minimizes an appropriate quasiconvex energy functional subject to the Jacobian constraint ${\rm det} \na u=1$ a.e., are necessarily Lipschitz. Furthermore we show that…

An energy for first-order structured deformations in the context of periodic homogenization is obtained. This energy, defined in principle by relaxation of an initial energy of integral type featuring contributions of bulk and interfacial…

We investigate variational problems in large-strain magnetoelasticity, both in the static and in the quasistatic setting. The model contemplates a mixed Eulerian-Lagrangian formulation: while deformations are defined on the reference…

Let $\mathbb{A}=\{z: r< |z|<R\}$ and $\A^\ast=\{z: r^\ast<|z|<R^\ast\}$ be annuli in the complex plane. Let $p\in[1,2]$ and assume that $\mathcal{H}^{1,p}(\A,\A^*)$ is the class of Sobolev homeomorphisms between $\A$ and $\A^*$, $h:\A\onto…

We investigate a variational theory for magnetoelastic solids under the incompressibility constraint. The state of the system is described by deformation and magnetization. While the former is classically related to the reference…

In a recent paper by Iglesias, Rumpf and Scherzer (Found. Comput. Math. 18(4), 2018) a variational model for deformations matching a pair of shapes given as level set functions was proposed. Its main feature is the presence of anisotropic…

We consider $\mathbb{S}^2$-valued maps on a domain $\Omega\subset\mathbb{R}^N$ minimizing a perturbation of the Dirichlet energy with vertical penalization in $\Omega$ and horizontal penalization on $\partial\Omega$. We first show the…

Given a closed submanifold, or a compact regular domain, in euclidean space, we consider the Riesz energy defined as the double integral of some power of the distance between pairs of points. When this integral diverges, we compare two…