Sobolev spaces for singular perturbation of 2D Laplace operator

被引：2

作者：

Georgiev, Vladimir ^{[1
,2
,3
]}

Rastrelli, Mario ^{[1
,2
]}

机构：

[1] Univ Pisa, Dept Math, Largo Bruno Pontecorvo 5, I-56127 Pisa, Italy

[2] Waseda Univ, Fac Sci & Engn, 3-4-1 Okubo,Shinjuku Ku, Tokyo 1698555, Japan

[3] Bulgarian Acad Sci, Inst Math & Informat, Acad G Bonchev Str Block 8, Sofia 1113, Bulgaria

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2025年 / 251卷

关键词：

Singular perturbation of Laplace operator; Sobolev spaces; Nonlinear Schrodinger equation; FRACTIONAL-POWERS; EQUATION;

D O I：

10.1016/j.na.2024.113710

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the perturbed Sobolev space H-alpha(1,r.), r is an element of(1, infinity), associated with singular perturbation Delta(alpha) of Laplace operator in Euclidean space of dimension 2. The main results give the possibility to extend the L-2 theory of perturbed Sobolev space to the L-r case. When r is an element of (2, infinity) we have appropriate representation of the functions in H-alpha(1,r.) in regular and singular part. An application to local well-posedness of the NLS associated with this singular perturbation in the mass critical and mass supercritical cases is established too.

引用

页数：24

共 31 条

[1] Existence, structure, and robustness of ground states of a NLSE in 3D with a point defect [J].