Related papers: Boundary regularity for manifold constrained $p(x)…

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 prove boundedness of rationally-connected threefolds in $\mathbb P^6$ under some extra-assumptions.

Motivated by problems arising in geometric flows, we prove several regularity results for systems of local and nonlocal equations, adapting to the parabolic case a neat argument due to Caffarelli. The geometric motivation of this work comes…

Let $M$ be a $C^2$-smooth Riemannian manifold with boundary and $N$ a complete $C^2$-smooth Riemannian manifold. We show that each stationary $p$-harmonic mapping $u\colon M\to N$, whose image lies in a compact subset of $N$, is locally…

We consider minimising $p$-harmonic maps from three-dimensional domains to the real projective plane, for $1<p<2$. These maps arise as least-energy configurations in variational models for nematic liquid crystals. We show that the singular…

Let $u$ be a solution to the normalized p-harmonic obstacle problem with $p>2$. That is, $u\in W^{1,p}(B_1(0))$, $2<p<\infty$, $u\ge 0$ and $$ \d\left( |\nabla u|^{p-2}\nabla u\right)=\chi_{\{u>0\}}\textrm{ in }B_1(0) $$ where $u(x)\ge 0$…

We prove that the composition of a quasi-nearly subharmonic function and a quasiregular mappings of bounded multiplicity is quasi-nearly subharmonic. Also, we prove that if $u\circ f$ is quasi-nearly subharmonic for all quasi-nearly…

This paper studies the structure and stability of boundaries in noncollapsed $\text{RCD}(K,N)$ spaces, that is, metric-measure spaces $(X,\mathsf{d},\mathscr{H}^N)$ with lower Ricci curvature bounded below. Our main structural result is…

We study biharmonic maps between conformally compact manifolds, a large class of complete manifolds with bounded geometry, asymptotically negative curvature, and smooth compactification. These metrics provide a far-reaching generalization…

In this paper we study on smooth bounded domains the global regularity (up to the boundary) for weak solutions to systems having $p$-structure depending only on the symmetric part of the gradient.

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…

In this paper, we study the convergence in the capacity of sequence of plurisubharmonic functions. As an application, we prove stability results for solutions of the complex Monge-Amp\`ere equations.

We define upper bound and lower bounds for order-preserving homogeneous of degree one maps on a proper closed cone in $\R^n$ in terms of the cone spectral radius. We also define weak upper and lower bounds for these maps. For a proper…

We construct N-harmonic functions in a domain with one isolated singularity on the boundary of the domain. By using solutions of the spherical p-harmonic spectral problem, we give an inductive method to produce a large variety of separable…

Let $f:X\times Y\times Z\longrightarrow W $ be a bounded tri-linear map on normed spaces. We say that $f$ is close-to-regular when $f^{t****s}=f^{s****t}$ and we say that $f$ is completely regular when all natural extensions are equal. In…

In this paper, as a continuation of [30], we consider the Gromov-Hausdorff convergence and collapsing in the family of compact Riemannian manifolds with boundary satisfying lower bounds on the sectional curvatures of interior manifolds,…

Suppose that $p \in (1,\infty]$, $\nu \in [1/2,\infty)$, $\mathcal{S}_\nu = \left\{ (x_1,x_2) \in \mathbb{R}^2 \setminus \{(0, 0)\}: |\phi| < \frac{\pi}{2\nu}\right\}$, where $\phi$ is the polar angle of $(x_1,x_2)$. Let $R>0$ and…

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…

Quasiconformal maps in the complex plane are homeomorphisms that satisfy certain geometric distortion inequalities; infinitesimally, they map circles to ellipses with bounded eccentricity. The local distortion properties of these maps give…

In this paper, we study the regularity of the solutions of Maxwell's equations in a bounded domain. We consider several different types of low regularity assumptions to the coefficients which are all less than Lipschitz. We first develop a…