Related papers: Harmonic maps between two concentric annuli in $\m…

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…

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…

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…

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 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…

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 consider rotationally symmetric $p$-harmonic maps from the unit disk $D^2\subset\real^2$ to the unit sphere $S^2\subset\real^3$, subject to Dirichlet boundary conditions and with $1<p<\infty$. We show that the associated energy…

The central theme of this paper is the variational analysis of homeomorphisms $h\colon \mathbb X \onto \mathbb Y$ between two given domains $\mathbb X, \mathbb Y \subset \mathbb R^n$. We look for the extremal mappings in the Sobolev space…

In this note, we study non-uniqueness for minimizing harmonic maps from $B^3$ to $\mathbb{S}^2$. We show that every boundary map can be modified to a boundary map that admits multiple minimizers of the Dirichlet energy by a small…

We consider the so called combined energy of a deformation between two concentric annuli and minimize it, provided that it keep order of the boundaries. It is an extension of the corresponding result of Euclidean energy. It is intrigue…

Given a complete doubling metric measure space $X$ that supports a $2$-Poincar\'e inequality, we approximate harmonic functions on a bounded domain $\Omega$ with a prescribed Newton-Sobolev boundary data. Our approach is based on the…

The study of singular perturbations of the Dirichlet energy is at the core of the phenomenological-description paradigm in soft condensed matter. Being able to pass to the limit plays a crucial role in the understanding of the…

We consider the problem of minimizing the weighted Dirichlet energy between homeomorphisms of planar annuli. A known challenge lies in the case when the weight $\lambda$ depends on the independent variable $z$. We prove that for an…

We study Dirichlet problems for harmonic maps from a Riemannian $m$-manifold $(M,g)$ into a Finsler $n$-manifold $(N, F)$. We assume that the dimension of the source manifold $M$ is less than or equal to 4, and that the finsler structure…

The paper establishes the existence of homeomorphisms between two planar domains that minimize the Dirichlet energy. Specifically, among all homeomorphisms f : R -> R* between bounded doubly connected domains such that Mod (R) < Mod (R*)…

The variational problem for the functional $F=\frac12\|\phi^*\omega\|_{L^2}^2$ is considered, where $\phi:(M,g)\to (N,\omega)$ maps a Riemannian manifold to a symplectic manifold. This functional arises in theoretical physics as the strong…

Given a half-harmonic map $u\in \dot H^{\frac{1}{2},2}(\mathbb{R},\mathbb{S}^1)$ minimizing the fractional Dirichlet energy under Dirichlet boundary conditions in $\mathbb{R}\setminus I$, we show the existence of a second half-harmonic map,…

We study the global Lipschitz character of minimisers of the Dirichlet energy of diffeomorphisms between doubly connected domains with smooth boundaries from Riemann surfaces. The key point of the proof is the fact that minimisers are…

The central theme in this paper is the Hopf-Laplace equation, which represents stationary solutions with respect to the inner variation of the Dirichlet integral. Among such solutions are harmonic maps. Nevertheless, minimization of the…

Let $N=(\Omega,\sigma)$ and $M=(\Omega^*,\rho)$ be doubly connected Riemann surfaces and assume that $\rho$ is a smooth metric with bounded Gauss curvature $\mathcal{K}$ and finite area. The paper establishes the existence of homeomorphisms…