Related papers: Boundary effects and weak$^*$ lower semicontinuity…
We study the mixing properties of a Brownian motion whose movements are hindered by semipermeable barriers. Our setting assumes that the process takes values in a smooth planar domain and that the barriers are one-dimensional closed curves.…
In this work, we establish the existence of mass-conserving weak solutions to a nonlinear collision-induced breakage equation in which binary collisions may trigger particle breakup. The result is proved for a class of product-type…
We prove that minimizers of variational integrals $$ \mathcal E(v)=\int_\Omega f(v)\quad\text{for }v\in\mathcal M(\Omega)\text{ such that } \mathscr{A} v=0, $$ are partially continuous provided that the integrands $f$ are strongly…
In the recent paper \cite{SER}, the second author proved a divergence-quasiconcavity inequality for the following functional $ \mathbb{D}(A)=\int_{\mathbb{T}^n} det(A(x))^{\frac{1}{n-1}}\,dx$ defined on the space of $p$-summable positive…
Nonlocal (spatial-dispersion) effects in multilayered metamaterials composed of periodic stacks of alternating, deeply subwavelength dielectric layers are known to be negligibly weak. Counterintuitively, under certain critical conditions,…
This paper has two goals: to present some new results that are necessary for further study and applications of quasi-linear functionals, and, by combining known and new results, to serve as a convenient single source for anyone interested…
For a fixed constant $\lambda > 0$ and a bounded Lipschitz domain $\Omega \subset \mathbb{R}^n$ with $n \geq 2$, we establish that almost-minimizers (functions satisfying a sort of variational inequality) of the Alt-Caffarelli type…
This article characterizes conjugates and subdifferentials of convex integral functionals over the linear space $\mathcal N^\infty$ of stochastic processes of essentially bounded variation (BV) when $\mathcal N^\infty$ is identified with…
In functional analysis, there are different notions of limit for a bounded sequence of $L^1$ functions. Besides the pointwise limit, that does not always exist, the behaviour of a bounded sequence of $L^1$ functions can be described in…
We introduce a family of (nonlinear) pairing measures that ensure the validity of the divergence rule for composite functions $\boldsymbol{B}(x,u(x))$, where $\boldsymbol{B}(\cdot,t)$ is a bounded divergence-measure vector field, and $u$ is…
We study the limit behaviour of a sequence of non-convex, vectorial, random integral functionals, defined on $W^{1,1}$, whose integrands satisfy degenerate linear growth conditions. These involve suitable random, scale-dependent…
The ballistic conductance through a device consisting of quantum wires, to which two stubs are attached laterally, is calculated assuming parabolic confining potentials of frequencies $\omega_w$ for the wires and $\omega_s$ for the stubs.…
We prove that any weakly differentiable function with square integrable gradient can be extended to a capacitary boundary of any simply connected plane domain $\Omega\ne\mathbb R^2$ except a set of a conformal capacity zero. For locally…
We study the backstepping stabilization of higher order linear and nonlinear Schr\"odinger equations on a finite interval, where the boundary feedback acts from the left Dirichlet boundary condition. The plant is stabilized with a…
Motivated by questions arising in the study of the spectral theory of models of aperiodic order, we investigate sums of functions of semibounded closed subsets of the real line. We show that under suitable thickness assumptions on the sets…
We study the semicontinuity of automorphism groups for perturbations of domains in complex space or in complex manifolds. We provide a new approach to the study of such results for domains having minimal boundary smoothness. The emphasis in…
The bounded variation seminorm and the Sobolev seminorm on compact manifolds are represented as a limit of fractional Sobolev seminorms. This establishes a characterization of functions of bounded variation and of Sobolev functions on…
A new extension of the sub-fractional Brownian motion, and thus of the Brownian motion, is introduced. It is a linear combination of a finite number of sub-fractional Brownian motions, that we have chosen to call the mixed sub-fractional…
We give partial boundary regularity for co-dimension one absolutely area-minimizing currents at points where the boundary consists of a sum of $C^{1,\alpha}$ submanifolds, possibly with multiplicity, meeting tangentially, given that the…
Recently the characterization of the compactness in the space $BV([0,1])$ of functions of bounded Jordan variation was given. Here, certain generalizations of this result are given for the spaces of functions of bounded Waterman…