44 citations · 253 across the 53 of their papers we have counts for
57 papers
Nonlocal convolution type functionals and related Orlicz spaces
Denis Borisov, Andrey Piatnitski
In the paper we introduce Orlicz type functional spaces defined in terms of nonlocal convolution type integral functionals and study the main properties of these spaces. We show in…
Homogenization of nonlocal equations in randomly evolving media. Diffusion approximation
Marina Kleptsyna, Andrey Piatnitski, Alexandre Popier
The paper deals with homogenization and higher order approximations of solutions to nonlocal evolution equations of convolution type whose coefficients are periodic in the spatial…
Homogenization of Lévy-type operators: operator estimates with correctors
Andrey Piatnitski, Vladimir Sloushch, Tatiana Suslina +1
The goal of the paper is to study in a self-adjoint operator ${\mathbb A}_\eps$, $\eps >0$, of the form $$ ({\mathbb A}_\eps u) (\x) = \int_{\R^d} μ(\x/\eps, \y/\eps) \…
Homogenisation and spectral convergence of high-contrast convolution type operators
Mikhail Cherdantsev, Andrey Piatnitski, Igor Velcic
The paper deals with homogenisation problems for high-contrast symmetric convolution-type operators with integrable kernels in media with a periodic microstructure. We adapt the tw…
Homogenization of non-symmetric convolution type operators
Andrey Piatnitski, Vladimir Sloushch, Tatiana Suslina +1
The paper studies homogenization problem for a bounded in convolution type operator ${\mathbb A}_\eps$, $\eps >0$, of the form $$ ({\mathbb A}_\eps u) (\x) = \ep…
Periodic homogenization of convolution type operators with heavy tails
Andrey Piatnitski, Elena Zhizhina
The paper deals with periodic homogenization of nonlocal symmetric convolution type operators in , whose kernel is the product of a density that belongs to the do…