Related papers: Periodic homogenization of convolution type operat…
In $L_2({\mathbb R}^3;{\mathbb C}^3)$, we consider a selfadjoint operator ${\mathcal L}_\varepsilon$, $\varepsilon >0$, given by the differential expression $\mu_0^{-1/2}\operatorname{curl} \eta(\mathbf{x}/\varepsilon)^{-1}…
In the first part, we obtain sharp results for L^2 boundedness of strongly singular operators on the Heisenberg group. We also define the oscillating convolution operators on the Heisenberg group and study their boundedness properties. In…
Metaplectic operators form a relevant class of operators appearing in different applications, in the present work we study their Schwartz kernels. Namely, diagonality of a kernel is defined by imposing rapid off-diagonal decay conditions,…
We introduce and study in a general setting the concept of homogeneity of an operator and, in particular, the notion of homogeneity of an integral operator. In the latter case, homogeneous kernels of such operators are also studied. The…
In this chapter we describe a selection of mathematical techniques and results that suggest interesting links between the theory of gratings and the theory of homogenization, including a brief introduction to the latter. By no means do we…
We study the homogenization for a class of non-symmetric pure jump Feller processes. The jump intensity involves periodic and aperiodic constituents, as well as oscillating and non-oscillating constituents. This means that the noise can…
This paper is devoted to the homogenization of Shr\"odinger type equations with periodically oscillating coefficients of the diffusion term, and a rapidly oscillating periodic time-dependent potential. One convergence theorem is proved and…
The periodic unfolding method is one of the latest tool after multi-scale convergence to study multi-scale problems like homogenization problems. It provides a good understanding of various micro scales involved in the problem which can be…
We consider the problem of the homogenization of non-local quadratic energies defined on $\delta$-periodic disconnected sets defined by a double integral, depending on a kernel concentrated at scale $\varepsilon$. For kernels with unbounded…
The topology of periodic spaces has attracted a lot of interest in recent years in order to study and classify crystalline structures and other large homogeneous data sets, such as the distribution of galaxies in cosmology. In practice,…
We derive, by means of variational techniques, a limiting description for a class of integral functionals under linear differential constraints. The functionals are designed to encode the energy of a high-contrast composite, that is, a…
In this paper, we establish some Harnack type inequalities satisfied by positive solutions of nonlocal inhomogeneous equations arising in the description of various phenomena ranging from population dynamics to micro-magnetism. For regular…
The dynamics of high partonic density QCD is presented considering, in the double logarithm approximation, the parton recombination mechanism built in the AGL formalism, developed including unitarity corrections for the nucleon as well for…
In the whole space $R^d$ ($d\ge 2$), we study homogenization of a divergence-form matrix elliptic operator $L_\varepsilon$ of an arbitrary even order larger than 2 with measurable $\varepsilon$-periodic coefficients, where $\varepsilon$ is…
We consider reversible vector fields in $\mathbb{R}^{2n}$ such that the set of fixed points of the involutory reversing symmetry is $n$-dimensional. Let such system have a smooth one-parameter family of symmetric periodic orbits which is of…
We demonstrate that the structure of complex second-order strongly elliptic operators $H$ on ${\bf R}^d$ with coefficients invariant under translation by ${\bf Z}^d$ can be analyzed through decomposition in terms of versions $H_z$,…
This paper concerns the rigorous periodic homogenization for a weakly coupled electroelastic system of a nonlinear electrostatic equation with an elastic equation enriched with electrostriction. Such coupling is employed to describe…
In $L_2({\mathbb R}^d;{\mathbb C}^n)$, we study a selfadjoint strongly elliptic operator $A_\varepsilon$ of order $2p$ given by the expression $b({\mathbf D})^* g({\mathbf x}/\varepsilon) b({\mathbf D})$, $\varepsilon >0$. Here $g({\mathbf…
Bilocal light-ray operators which are Lorentz scalars, vectors or antisymmetric tensors, and which appear in various hard scattering QCD processes, are decomposed into operators of definite twist. These operators are harmonic tensor…
The stabilization of Hochschild homology of commutative algebras is Gamma homology. We describe a cyclic variant of Gamma homology and prove that the associated analogue of Connes' periodicity sequence becomes almost trivial, because the…