Arkady Poliakovsky

Coupling of order parameters, chirality, and interfacial structures in multiferroic materials

We study optimal interfacial structures in multiferroic materials with a biquadratic coupling between two order parameters. We discover a new duality relation between the strong coupling and the weak coupling regime for the case of isotropic gradient terms. We analyze the phase diagram depending on the coupling constant and anisotropy of the gradient term, and show that in a certain regime the secondary order parameter becomes activated only in the interfacial region.

Upper bounds for singular perturbation problems involving gradient fields

We prove an upper bound for the Aviles-Giga problem, which involves the minimization of the energy

Uniqueness of positive solutions for singular problems involving the p-laplacian

E_\e(v)=\e\int_\Omega\big|\nabla^2v\big|^2dx+\frac{1}{\e}\int_\Omega\big(1-|\nabla v|^2\big)^2dx

On minimization problems which approximate Hardy Lp inequality

over

Jump detection in Besov spaces via a new BBM formula. Applications to Aviles–Giga-type functionals

v\in H^2(\Omega)

On the Γ-limit of singular perturbation problems with optimal profiles which are not one-dimensional. Part II: The lower bound

, where

Variational resolution for some general classes of nonlinear evolutions. Part I

\e>0

Variational resolution for some general classes of nonlinear evolutions. Part II

is a small parameter. Given

ON THE RELATION BETWEEN MINIMIZERS OF A Γ-LIMIT ENERGY AND OPTIMAL LIFTING IN BV-SPACE

v\in W^{1,\infty}(\Omega)

On a planar Liouville-type problem in the study of selfgravitating strings

such that