Related papers: Bloch estimates in non-doubling generalized Orlicz…

We study universal approximation of continuous functionals on compact subsets of products of Hilbert spaces. We prove that any such functional can be uniformly approximated by models that first take finitely many continuous linear…

The sample paths of Brownian motion are known to admit the exact Besov-type smoothness exponent 1/2 when measured in the sub-Gaussian Orlicz norm. We extend these regularity results by deriving the exact limit of the sub-Gaussian Orlicz…

We prove the local Lipschitz regularity of the local minimizers of scalar integral functionals of the form \begin{equation*} \mathcal{F}(v;\Omega)= \int_{\Omega} f (x, Dv) dx \end{equation*} under $(p,q)$-growth conditions. The main novelty…

We consider a generalization of the classic linear regression problem to the case when the loss is an Orlicz norm. An Orlicz norm is parameterized by a non-negative convex function $G:\mathbb{R}_+\rightarrow\mathbb{R}_+$ with $G(0)=0$: the…

We study the existence of very weak solutions to a system \[\begin{cases}-\mathrm{div} \mathcal{A}(x,D\mathbf{u})=\mathbf{\mu}\quad\text{in }\ \Omega, \mathbf{u}=0\quad\text{on }\ \partial\Omega\end{cases} \] with a datum $\mathbf{\mu}$…

We prove an a priori estimate for the second derivatives of local minimizers of integral functionals of calculus of variation with convex integrand with respect to the gradient variable, assuming that the function that measures the…

In this paper we introduce a new approach for approximately counting in bounded degree systems with higher-order constraints. Our main result is an algorithm to approximately count the number of solutions to a CNF formula $\Phi$ when the…

We consider the estimation of two-sample integral functionals, of the type that occur naturally, for example, when the object of interest is a divergence between unknown probability densities. Our first main result is that, in wide…

We study sharp growth conditions for the boundedness of the Hardy-Littlewood maximal function in the generalized Orlicz spaces. We assume that the generalized Orlicz function $\phi(x, t)$ satisfies the standard continuity properties (A0),…

Let $\mathcal{X}$ be a space of homogenous type and $\varphi:\ \mathcal{X}\times[0,\infty) \to[0,\infty)$ a growth function such that $\varphi(\cdot,t)$ is a Muckenhoupt weight uniformly in $t$ and $\varphi(x,\cdot)$ an Orlicz function of…

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…

In this paper, we provide a unifying theory concerning the convergence properties of the so-called max-product Kantorovich sampling operators based upon generalized kernels in the setting of Orlicz spaces. The approximation of functions…

We prove existence of renormalized solutions to general nonlinear elliptic equation in Musielak-Orlicz space avoiding growth restrictions. Namely, we consider \begin{equation*} -{\rm div} A(x,\nabla u)= f\in L^1(\Omega), \end{equation*} on…

Majorization-minimization schemes are a broad class of iterative methods targeting general optimization problems, including nonconvex, nonsmooth and stochastic. These algorithms minimize successively a sequence of upper bounds of the…

We study existence, unicity and other geometric properties of the minimizers of the energy functional $$ \|u\|^2_{H^s(\Omega)}+\int_\Omega W(u)\,dx, $$ where $\|u\|_{H^s(\Omega)}$ denotes the total contribution from $\Omega$ in the $H^s$…

We study the minimizers of a functional on the set of partitions of a domain $\Omega \subset R^n$ into $N$ subsets $W_j$ of locally finite perimeter in $\Omega$, whose main term is $\sum_{j=1^N} \int_{\Omega \cap \partial W_j} a(x)…

In this article, we investigate the existence of closed vector subspaces (i.e.spaceability) in various nonlinear subsets of Orlicz-Lorentz spaces $\Lambda_{\varphi,w}$, equipped with the Luxemburg norm. If a family of Orlicz functions…

We prove a new type of pointwise estimate of the Kalamajska-Mazya-Shaposhnikova type, where sparse averaging operators replace the maximal operator. It allows us to extend the Gagliardo-Nirenberg interpolation inequality to all…

We consider uniformly elliptic operators with Dirichlet or Neumann homogeneous boundary conditions on a domain $\Omega $ in ${\mathbb{R}}^N$. We consider deformations $\phi (\Omega)$ of $\Omega $ obtained by means of a locally Lipschitz…

We study the following boundary value problem (P)\ \ \ \ \ {-\mathrm{div}(a(|\nabla u|)\nabla u)=f(x,u),\ & in $\Omega$, u=0, & on $\partial\Omega$} with nonhomogeneous principal part. By assuming the nonlinearity $f(x, t)$ being…