M. Rastrelli

activity

20232026

collaborators

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4 papers · 1 filter

math.AP2026

Standing waves for defocusing nonlinear Schrödinger equations with point interaction

Noriyoshi Fukaya, Yuki Osada, Mario Rastrelli

We consider standing waves of the nonlinear Schrödinger equation $i \partial_{t} u = - Δ_{α} u + ∣ u ∣^{p - 1} u$ in the defocusing case in dimensions $N = 2$ and $N = 3$ . Here, $- Δ_{α}$ denotes the…

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.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…

Standing waves for defocusing nonlinear Schrödinger equations with point interaction

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

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 $R^{2}$