Elliptic Schrödinger Equations with Gradient-Dependent
Nonlinearity and Hardy Potential Singular on Manifolds

J 2025

Elliptic Schrödinger Equations with Gradient-Dependent Nonlinearity and Hardy Potential Singular on Manifolds

GKIKAS, Konstantinos T. a Phuoc Tai NGUYEN

Základní údaje

Originální název

Elliptic Schrödinger Equations with Gradient-Dependent Nonlinearity and Hardy Potential Singular on Manifolds

Autoři

GKIKAS, Konstantinos T. a Phuoc Tai NGUYEN (704 Vietnam, garant, domácí)

Vydání

Journal of Geometric Analysis, Springer, 2025, 1050-6926

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 1.200 v roce 2023

Organizační jednotka

Přírodovědecká fakulta

DOI

http://dx.doi.org/10.1007/s12220-025-02046-9

UT WoS

001503680400002

EID Scopus

2-s2.0-105007446706

Klíčová slova anglicky

Hardy potentials; Gradient-dependent nonlinearities; Boundary trace; Capacities

Štítky

rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 26. 6. 2025 12:51, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

Let \Omega \subset {\mathbb {R}}^N N \ge 3 be a C^2 bounded domain and \Sigma \subset \Omega is a C^2 compact boundaryless submanifold in {\mathbb {R}}^N of dimension k, 0\le k < N-2. For \mu \le (\frac{N-k-2}{2})^2, put L_\mu := \Delta + \mu d_{\Sigma }^{-2} where d_{\Sigma }(x) = \textrm{dist}(x,\Sigma ). We study boundary value problems for equation -L_\mu u = g(u,|\nabla u|) in \Omega \setminus \Sigma, subject to the boundary condition u=\nu on \partial \Omega \cup \Sigma, where g: {\mathbb {R}} \times {\mathbb {R}}_+ \rightarrow {\mathbb {R}}_+ is a continuous and nondecreasing function with g(0,0)=0, \nu is a given nonnegative measure on \partial \Omega \cup \Sigma. When g satisfies a so-called subcritical integral condition, we establish an existence result for the problem under a smallness assumption on \nu. If g(u,|\nabla u|) = |u|^p|\nabla u|^q, there are ranges of p, q, called subcritical ranges, for which the subcritical integral condition is satisfied, hence the problem admits a solution. Beyond these ranges, where the subcritical integral condition may be violated, we establish various criteria on \nu for the existence of a solution to the problem expressed in terms of appropriate Bessel capacities.

Návaznosti

GA22-17403S, projekt VaV

Název: Nelineární Schrödingerovy rovnice a systémy se singulárním potenciálem (Akronym: NSESSP)

Investor: Grantová agentura ČR, Nonlinear Schrödinger equations and systems with singular potentials

Citovat

GKIKAS, Konstantinos T. a Phuoc Tai NGUYEN. Elliptic Schrödinger Equations with Gradient-Dependent Nonlinearity and Hardy Potential Singular on Manifolds. Journal of Geometric Analysis. Springer, 2025, roč. 35, č. 7, s. 212-257. ISSN 1050-6926. Dostupné z: https://dx.doi.org/10.1007/s12220-025-02046-9.

@article{2505727,
   author = {Gkikas, Konstantinos T. and Nguyen, Phuoc Tai},
   article_number = {7},
   doi = {http://dx.doi.org/10.1007/s12220-025-02046-9},
   keywords = {Hardy potentials; Gradient-dependent nonlinearities; Boundary trace; Capacities},
   language = {eng},
   issn = {1050-6926},
   journal = {Journal of Geometric Analysis},
   title = {Elliptic Schrödinger Equations with Gradient-Dependent Nonlinearity and Hardy Potential Singular on Manifolds},
   url = {https://doi.org/10.1007/s12220-025-02046-9},
   volume = {35},
   year = {2025}
}

TY  - JOUR
ID  - 2505727
AU  - Gkikas, Konstantinos T. - Nguyen, Phuoc Tai
PY  - 2025
TI  - Elliptic Schrödinger Equations with Gradient-Dependent Nonlinearity and Hardy Potential Singular on Manifolds
JF  - Journal of Geometric Analysis
VL  - 35
IS  - 7
SP  - 212
EP  - 212
PB  - Springer
SN  - 10506926
KW  - Hardy potentials
KW  - Gradient-dependent nonlinearities
KW  - Boundary trace
KW  - Capacities
UR  - https://doi.org/10.1007/s12220-025-02046-9
N2  - Let \Omega \subset {\mathbb {R}}^N N \ge 3 be a C^2 bounded domain and \Sigma \subset \Omega is a C^2 compact boundaryless submanifold in {\mathbb {R}}^N of dimension k, 0\le k < N-2. For \mu \le (\frac{N-k-2}{2})^2, put L_\mu := \Delta + \mu d_{\Sigma }^{-2} where d_{\Sigma }(x) = \textrm{dist}(x,\Sigma ). We study boundary value problems for equation -L_\mu u = g(u,|\nabla u|) in \Omega \setminus \Sigma, subject to the boundary condition u=\nu on \partial \Omega \cup \Sigma, where g: {\mathbb {R}} \times {\mathbb {R}}_+ \rightarrow {\mathbb {R}}_+ is a continuous and nondecreasing function with g(0,0)=0, \nu is a given nonnegative measure on \partial \Omega \cup \Sigma. When g satisfies a so-called subcritical integral condition, we establish an existence result for the problem under a smallness assumption on \nu. If g(u,|\nabla u|) = |u|^p|\nabla u|^q, there are ranges of p, q, called subcritical ranges, for which the subcritical integral condition is satisfied, hence the problem admits a solution. Beyond these ranges, where the subcritical integral condition may be violated, we establish various criteria on \nu for the existence of a solution to the problem expressed in terms of appropriate Bessel capacities.
ER  -

GKIKAS, Konstantinos T. a Phuoc Tai NGUYEN. Elliptic Schrödinger Equations with Gradient-Dependent Nonlinearity and Hardy Potential Singular on Manifolds. \textit{Journal of Geometric Analysis}. Springer, 2025, roč.~35, č.~7, s.~212-257. ISSN~1050-6926. Dostupné z: https://dx.doi.org/10.1007/s12220-025-02046-9.

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