Related papers: A limiting case in partial regularity for quasicon…

Consider a bounded, strongly pseudoconvex domain $D\subset \mathbb C^n$ with minimal smoothness (namely, the class $C^2$) and let $b$ be a locally integrable function on $D$. We characterize boundedness (resp., compactness) in $L^p(D), p >…

In this paper, we consider a class of variational problems with integral functionals involving nonlocal gradients. These models have been recently proposed as refinements of classical hyperelasticity, aiming for an effective framework to…

We consider the minimization property of a Gagliardo-Slobodeckij seminorm which can be seen as the fractional counterpart of the classical problem of functions of least gradient and which is related to the minimization of the nonlocal…

Given an analytic function $f=u+iv$ in the unit disk $\mathbb{D}$, Zygmund's theorem gives the minimal growth restriction on $u$ which ensures that $v$ is in the Hardy space $h^1$. This need not be true if $f$ is a complex-valued harmonic…

We investigate surfaces with bounded L^p-norm of the fractional mean curvature, a quantity we shall refer to as fractional Willmore-type functional. In the subcritical case and under convexity assumptions we show how this…

We present a systematic study on a class of nonlocal integral functionals for functions defined on a bounded domain and the naturally induced function spaces. The function spaces are equipped with a seminorm depending on finite differences…

In [David-Toro 15] and [David-Engelstein-Toro 19], (some of) the authors studied almost minimizers for functionals of the type first studied by Alt and Caffarelli in [Alt-Caffarelli 81] and Alt, Caffarelli and Friedman in…

We provide a general treatment of perturbations of a class of functionals modeled on convolution energies with integrable kernel which approximate the $p$-th norm of the gradient as the kernel is scaled by letting a small parameter…

We study the behaviour of linear partial differential operators with polynomial coefficients via a Wigner type transform. In particular, we obtain some results of regularity in the Schwartz space $\mathcal S$ and in the space ${\mathcal…

Let $u(x,y)$ be a harmonic function in the halfspace $\mathbb{R}^n\times\mathbb{R}_+$ that grows near the boundary not faster than some fixed majorant $w(y)$. Recently it was proven that an appropriate weighted average along the vertical…

We prove higher differentiability of bounded local minimizers to some widely degenerate functionals, verifying superquadratic anisotropic growth conditions. In the two dimensional case, we prove that local minimizers to a model functional…

We investigate Lindel\"of and Koebe type boundary behavior results for bounded quasiregular mappings in $n$-dimensional Euclidean space. Our results give sufficient conditions for the existence of non-tangential limits at a boundary point.

We study almost minimizers for the thin obstacle problem with variable H\"older continuous coefficients and zero thin obstacle and establish their $C^{1,\beta}$ regularity on the either side of the thin space. Under an additional assumption…

In this short note, we consider quasiregular local homeomorphisms on uniform domains. We prove that such mappings always can be extended to some boundary points along John curves, which extends the corresponding result of Rajala [Amer. J.…

Let $D$ be an bounded region in ${\bf R}^n$. The regularity of solutions of a family of quasilinear elliptic partial differential equations is studied, one example being $\Delta_nu=Vu^{n-1}$. The coefficients are assumed to be in the space…

By methods of harmonic analysis, we identify large classes of Banach spaces invariant of periodic Fourier multipliers with symbols satisfying the classical Marcinkiewicz type conditions. Such classes include general (vector-valued) Banach…

We show that the subgradient method converges only to local minimizers when applied to generic Lipschitz continuous and subdifferentially regular functions that are definable in an o-minimal structure. At a high level, the argument we…

An extension of Marcinkiewicz Interpolation Theorem, allowing intermediate spaces of Orlicz type, is proved. This generalization yields a necessary and sufficient condition so that every quasilinear operator, which maps the set, $S(X,\mu)$,…

Multiscale periodic homogenization is extended to an Orlicz-Sobolev setting. It is shown by the reiteraded periodic two-scale convergence method that the sequence of minimizers of a class of highly oscillatory minimizations problems…

We establish the local Lipschitz regularity of the local minimizers of non autonomous integral funtionals of the form \[ \int_\Omega F(x, Dz)\,dx, \] where $\Omega$ is a bounded open set of $\mathbb{R}^n$, $n \ge 2$. The energy density…