8 papers
Very weak solutions of the heat equation with anisotropically singular time-dependent diffusivity
Zhirayr Avetisyan, Zahra Keyshams, Monire Mikaeili Nia +1
We investigate the heat equation with a time-dependent, anisotropic, and potentially singular diffusivity tensor. Since weak (in the Sobolev sense) or distributional solutions may…
Reproducing Kernel Hilbert Spaces and entropy Kolmogorov numbers on compact Lie Groups
Zhirayr Avetisyan, Michael Ruzhansky, Karina Gonzalez
On a compact Lie group , we consider the reproducing kernel Hilbert space associated with the integral kernel of a left-invariant, positive, symmetric, trace…
Exponential decay estimates for the resolvent kernel on a Riemannian manifold
Zhirayr Avetisyan
On a complete, connected, non-compact Riemannian manifold, with Ricci curvature bounded from below, we establish exponential decay estimates at infinity for the spherical sums of t…
Very weak solutions of the heat equation with anisotropically singular time-dependent diffusivity
Zhirayr Avetisyan, Zahra Keyshams, Monire Mikaeili Nia +1
We investigate the heat equation with a time-dependent, anisotropic, and potentially singular diffusivity tensor. Since weak (in the Sobolev sense) or distributional solutions may…
On a unique two-dimensional integral operator homogeneous with respect to all orientation preserving linear transformations
Zhirayr Avetisyan, Alexey Karapetyants, Adolf Mirotin
In this paper, we consider a two-dimensional operator with an antisymmetric integral kernel, recently introduced by Z. Avetisyan and A. Karapetyants in connection to the study of g…
Parabolic equations with concave non-linearity
Zhirayr Avetisyan, Khachatur Khachatryan, Michael Ruzhansky
In this paper we prove the existence and uniqueness of positive mild solutions for the semilinear parabolic equations of the form , where is a p…