Vladimir Georgiev

activity

20232025

collaborators

4 papers

math.AP2025

Fractional Sobolev Spaces for the Singular-perturbed Laplace Operator in the $L^{p}$ setting

Vladimir Georgiev, Mario Rastrelli

We study the perturbed Sobolev spaces $H_{α}^{s, p} (R^{d})$ , associated with singular perturbation $Δ_{α}$ of Laplace operator in Euclidean space of dimensions 2 and 3. We exte…

math.AP2025

On the Cauchy problem for the reaction-diffusion system with point-interaction in $R^{2}$

Daniele Barbera, Vladimir Georgiev, Mario Rastrelli

The paper studies the existence of solutions for the reaction-diffusion equation in $R^{2}$ with point-interaction laplacian $Δ_{α}$ with $α \in (- \infty, + \infty]$ , assuming the…

math.AP2024

Solutions for fourth order anisotropic nonlinear Schrödinger equations in $R^{2}$

Vladimir Georgiev, Tianxiang Gou

In this paper, we consider solutions to the following fourth order anisotropic nonlinear Schrödinger equation in $R \times R^{2}$ , $$ \left\{ \begin{aligned} &\textnormal{i}\partia…

math.AP2023

Sobolev spaces for singular perturbation of Laplace operato

Vladimir Georgiev, Mario Rastrelli

We study the perturbed Sobolev space $H_{α}^{1, r}$ , $r \in (1, \infty),$ associated with singular perturbation $Δ_{α}$ of Laplace operator in Euclidean space of dimension $2.$ The main…

Fractional Sobolev Spaces for the Singular-perturbed Laplace Operator in the Lp setting

On the Cauchy problem for the reaction-diffusion system with point-interaction in R2

Solutions for fourth order anisotropic nonlinear Schrödinger equations in R2

Sobolev spaces for singular perturbation of Laplace operato

Fractional Sobolev Spaces for the Singular-perturbed Laplace Operator in the $L^{p}$ setting

On the Cauchy problem for the reaction-diffusion system with point-interaction in $R^{2}$

Solutions for fourth order anisotropic nonlinear Schrödinger equations in $R^{2}$