Related papers: n/p-Harmonic maps: regularity for the sphere case

In the present paper, we study the Poincare map associated to a periodic perturbation, both in space and time, of a linear Hamiltonian system. The dynamical system embodies the essential physics of stellar pulsations and provides a global…

We study regularity of minimizing $p$-harmonic maps $u \colon B^3 \to \mathbb{S}^3$ for $p$ in the interval $[2,3]$. For a long time, regularity was known only for $p = 3$ (essentially due to Morrey) and $p = 2$ (Schoen-Uhlenbeck), but…

We show that a if a Riemannian manifold admits a universal cover with bounded geometry and if 0 does not belong to the spectrum or is an isolated point in the spectrum of the Laplacian on $\ell$-forms, then there exists $1<p<2$ such that…

Let $X$ be a compact real algebraic set of dimension $n$. We prove that every Euclidean continuous map from $X$ into the unit $n$-sphere can be approximated by regulous map. This strengthens and generalizes previously known results.

We study a new class of Fourier integral operators defined in R^N. Their symbols are allowed to satisfy a differential inequality with certain multi-parameter characteristic. We prove these operators of order -(N-1)/2 bounded from the…

Motivated by the theory of harmonic maps on Riemannian surfaces, conformal-harmonic maps between two Riemannian manifolds $M$ and $N$ were introduced in search of a natural notion of harmonicity for maps defined on a general even…

In this paper, we will study the partial regularity theorem for stationary harmonic maps from a Riemannian manifold into a Lorentzian manifold. For a weakly stationary harmonic map $(u,v)$ from a smooth bounded open domain…

In this article, we study harmonic symmetries on the compact locally conformally K\"{a}hler manifold $M$ of $dim_{\mathbb{C}}=n$. The space of harmonic symmetries is a subspace of harmonic differential forms which defined by the kernel of a…

We present an extension of an algorithm for the classical scalar $p$-Laplace Dirichlet problem to the vector-valued $p$-Laplacian with mixed boundary conditions in order to solve problems occurring in shape optimization using a $p$-harmonic…

In this article we introduce a natural extension of the well-studied equation for harmonic maps between Riemannian manifolds by assuming that the target manifold is equipped with a connection that is metric but has non-vanishing torsion.…

We introduce the notion of a regular mapping on a non-commutative $L_p$-space associated to a hyperfinite von Neumann algebra for $1\le p\le \infty$. This is a non-commutative generalization of the notion of regular or order bounded map on…

In this paper, we first obtain an $L^q$ gradient estimate for $p$-harmonic maps, by assuming the target manifold supporting a certain function, whose gradient and Hessian satisfy some analysis conditions. From this $L^q$ gradient estimate,…

We consider the equation $-\Delta_p u=f(u)$ in a smooth bounded domain of $\mathbb{R}^n $, where $\Delta_p$ is the $p$-Laplace operator. Explicit examples of unbounded stable energy solutions are known if $n\geq p+4p/(p-1)$. Instead, when…

J.Eells and L. Lemaire introduced k-harmonic maps, and T. Ichiyama, J. Inoguchi and H.Urakawa showed the first variation formula. In this paper, we give the second variation formula of k-harmonic maps, and show non-existence theorem of…

We prove the local Lipschitz continuity of sub-elliptic harmonic maps between certain singular spaces, more specifically from the $n$-dimensional Heisenberg group into $CAT(0)$ spaces. Our main theorem establishes that these maps have the…

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…

By seeing whether a Liouville type theorem holds for positive, bounded, and/or finite energy $p$-harmonic and $p$-quasiharmonic functions, we classify proper metric spaces equipped with a locally doubling measure supporting a local…

We prove a general perturbation theorem that can be used to obtain pairs of nontrivial solutions of a wide range of local and nonlocal nonhomogeneous elliptic problems. Applications to critical $p$-Laplacian problems, $p$-Laplacian problems…

In this paper, we introduce a class of complex-valued polyharmonic mappings, denoted by $HS_{p}(\lambda)$, and its subclass $HS_{p}^{0}(\lambda)$, where $\lambda\in [0,1]$ is a constant. These classes are natural generalizations of a class…

In this work we develop a nonlinear decomposition, associated with nonlinear eigenfunctions of the p-Laplacian for p \in (1, 2). With this decomposition we can process signals of different degrees of smoothness. We first analyze solutions…