Related papers: Examples of $p$-harmonic maps

$\infty$-Harmonic maps are a generalization of $\infty$-harmonic functions. They can be viewed as the limiting cases of p-harmonic maps as p goes to infinity. In this paper, we give complete classifications of linear and quadratic…

We propose a new notion called \emph{infinity-harmonic maps}between Riemannain manifolds. These are natural generalizations of the well known notion of infinity harmonic functions and are also the limiting case of $p$% -harmonic maps as…

The aim of this paper is to study some examples of exponentially harmonic maps. We study such maps firstly on flat euclidean and Minkowski spaces and secondly on Friedmann-Lema\^ itre universes. We also consider some new models of…

Adapting \cite{strz3}, we define generalized $p$-harmonic maps into Riemannian homogeneous targets, a notion of solutions not belonging to the energy space. Restricting our attention to the subcritical range $p$ greater than the domain…

Harmonic maps are nonlinear extensions of harmonic functions. They are critical points of natural energy functionals between Riemannian manifolds. Such type of problems appear in Physics, Geometry of Finance and the study of regularity and…

For any $n \geq 3$ and any closed manifold $\mathcal{N}$ with $\pi_{n+k}(\mathcal{N}) \neq \{0\}$ for some $k \geq 0$, we establish the existence of nontrivial $n$-harmonic maps from $\mathbb{S}^n$ into $\mathcal{N}$. When $k\geq 1$, these…

We discuss various representations of planar $p$-harmonic systems of equations and their solutions. For coordinate functions of $p$-harmonic maps we analyze signs of their Hessians, the Gauss curvature of $p$-harmonic surfaces, the length…

In this paper, we extend the definition of p-harmonic and p-biharmonic maps between Riemannian manifolds. We present some new properties for the generalized stable p-harmonic maps.

We prove the uniqueness of solutions to Dirichlet problem for p-harmonic maps with images in a small geodesic ball of the target manifold. As a consequence, we show that such maps have Hoelder continuous derivatives. This gives an extension…

We prove that, in general, given a $p$-harmonic map $F:M\to N$ and a convex function $H:N\to\mathbb{R}$, the composition $H\circ F$ is not $p$-subharmonic. By assuming some rotational symmetry on manifolds and functions, we reduce the…

In this work, we extend the concepts of $p$-biharmonic maps and $p$-biharmonic hypersurfaces to provide a broader characterization of $(p,q)$-harmonic hypersurfaces and $(p,q)$-harmonic curves in Riemannian manifolds, including Einstein…

We prove partial and full boundary regularity for manifold constrained $p(x)$-harmonic maps.

We construct and analyze solutions to a regularized homogeneous $p$-harmonic map flow equation for general $p \geq 2$. The homogeneous version of the problem is new and features a monotonicity formula extending the one found by Struwe for…

In this note, we extend the definition of $p$-biharmonic and bi-$p$-harmonic maps between two Riemannian manifolds and explore some of their properties.

A direct relation between the enumeration of ordinary maps and that of fully simple maps first appeared in the work of the first and last authors. The relation is via monotone Hurwitz numbers and was originally proved using Weingarten…

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…

We derive the sharp vectorial Kato inequality for $p$-harmonic mappings. Surprisingly, the optimal constant differs from the one obtained for scalar valued $p$-harmonic functions by Chang, Chen, and Wei. As an application we demonstrate how…

We study a second order ordinary differential equation corresponding to rotationally symmetric $p$-harmonic maps. We show unique continuation and Liouville's type theorems for positive solutions. We discuss the existence of bounded positive…

Assume that $p\in(1,\infty]$ and $u=P_{h}[\phi]$, where $\phi\in L^{p}(\mathbb{S}^{n-1},\mathbb{R}^{n})$. Then for any $x\in \mathbb{B}^{n}$, we obtain the sharp inequalities $$ |u(x)|\leq…

In this two papers we deal with the relative homotopy Dirichlet problem for p-harmonic maps from compact manifolds with boundary to manifolds of non-positive sectional curvature. Notably, we give a complete solution to the problem in case…