Related papers: Orlicz-Sobolev versus H\"older local minimizer for…

We prove uniform parabolic H\"older estimates of De Giorgi-Nash-Moser type for sequences of minimizers of the functionals \[ \mathcal{E}_\varepsilon(W) = \int_0^\infty \frac{e^{- t/\varepsilon}}{\varepsilon} \bigg\{…

In this paper, we study the interplay between Orlicz-Sobolev spaces $L^{M}$ and $W^{1,M}$ and fractional Sobolev spaces $W^{s,p}$. More precisely, we give some qualitative properties of the new fractional Orlicz-Sobolev space $W^{s,M}$,…

In this paper, we first prove the existence of solutions to Dirichlet problems involving the fractional $g$-Laplacian operator and lower order terms by appealing to sub- and supersolution methods. Moreover, we also state the existence of…

In this paper we study the fractional p(., .)-Laplacian and we introduce the corresponding nonlocal conormal derivative for this operator. We prove basic properties of the corresponding function space and we establish a nonlocal version of…

In this paper, we study the regularity of weak solutions and subsolutions of second-order elliptic equations having a gradient term with superquadratic growth. We show that, under appropriate integrability conditions on the data, all weak…

The aim of this paper is to study the heterogeneous optimization problem \begin{align*} \mathcal {J}(u)=\int_{\Omega}(G(|\nabla u|)+qF(u^+)+hu+\lambda_{+}\chi_{\{u>0\}} )\text{d}x\rightarrow\text{min}, \end{align*} in the class of functions…

We show that if $\mathbb{R}^{n}$ is equipped with certain non-doubling metric and an Orlicz-Sobolev inequality holds for a special family of Young functions $\Phi $, then weak solutions to quasilinear infinitely degenerate elliptic…

We prove H\"older regularity estimates up to the boundary for weak solutions $u$ to nonlocal Schr\"odinger equations subject to exterior Dirichlet conditions in an open set $\Omega\subset \mathbb{R}^N$. The class of nonlocal operators…

We give an alternative proof for H\"older regularity for weak solutions of nonlocal elliptic quasilinear equations modelled on the fractional p-Laplacian where we replace the discrete De Giorgi iteration on a sequence of concentric balls by…

Let $\Omega\subset\dR^d$ be a bounded or an unbounded Lipschitz domain. In this note we address the problem of continuation of functions from the Sobolev space $H^1(\Omega)$ up to functions in the Sobolev space $H^1(\dR^d)$ via a linear…

We prove $C^{1,\nu}$ regularity for local minimizers of the \oh{multi-phase} energy: \begin{flalign*} w \mapsto \int_{\Omega}\snr{Dw}^{p}+a(x)\snr{Dw}^{q}+b(x)\snr{Dw}^{s} \ dx, \end{flalign*} under sharp assumptions relating the couples…

We consider equations involving a combination of local and nonlocal degenerate $p$-Laplace operators. The main contribution of the paper is almost Lipschitz regularity for the homogeneous equation and H\"older continuity with an explicit…

We study the regularity of solutions to the fully nonlinear thin obstacle problem. We establish local $C^{1,\alpha}$ estimates on each side of the smooth obstacle, for some small $\alpha > 0$. Our results extend those of Milakis-Silvestre…

In this paper we address the problem of the minimization of the $k$-th Robin eigenvalue $\lambda_{k,\beta}$ with parameter $\beta>0$ among bounded open Lipschitz sets with prescribed perimeter. The perimeter constraint allows us to…

In this paper we prove compact embedding of a subspace of the fractional Orlicz-Sobolev space $W^{s, G}\left(\mathbb{R}^{N}\right)$ consisting of radial functions, our target embedding spaces are of Orlicz type. Also, we prove a Lions and…

We consider Orlicz--Laplace equation $-div(\frac{\varphi'(|\nabla u|)}{|\nabla u|}\nabla u)=f$ where $\varphi$ is an Orlicz function and either $f=0$ or $f\in L^\infty$. We prove local second order regularity results for the weak solutions…

In this paper, we develop some properties of the $a_{x,y}(.)$-Neumann derivative for the fractional $a_{x,y}(.)$-Laplacian operator. Therefore we prove the basic proprieties of the correspondent function spaces. In the second part of this…

We consider regularity issues for minima of non-autonomous functionals in the Calculus of Variations exhibiting non-uniform ellipticity features. We provide a few sharp regularity results for local minimizers that also cover the case of…

We consider linear and obstacle problems driven by a nonlocal integral operator, for which nonlocal interactions are restricted to a ball of finite radius. These type of operators are used to model anomalous diffusion and, for a special…

We consider nonlinear equations having generalized Orlicz growth (also known as Musielak--Orlicz growth). We prove that if differential operators $\mathcal{A}_i$ converge locally uniformly to an operator $\mathcal{A}$, then the sequence of…