Poisson problems involving fractional Hardy operators and
measures

J 2023

Poisson problems involving fractional Hardy operators and measures

CHEN, Huyuan; Konstantinos T. GKIKAS a Phuoc-Tai NGUYEN

Základní údaje

Originální název

Poisson problems involving fractional Hardy operators and measures

Autoři

CHEN, Huyuan; Konstantinos T. GKIKAS a Phuoc-Tai NGUYEN

Vydání

Nonlinearity, IOP Publishing Ltd, 2023, 0951-7715

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Velká Británie a Severní Irsko

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 1.600

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/23:00134388

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova anglicky

Poisson problem; fractional hardy Laplacian; Radon measure; Kato's inequality

Štítky

14311010, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 23. 1. 2024 13:30, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

In this paper, we study the Poisson problem involving a fractional Hardy operator and a measure source. The complex interplay between the nonlocal nature of the operator, the peculiar effect of the singular potential and the measure source induces several new fundamental difficulties in comparison with the local case. To overcome these difficulties, we perform a careful analysis of the dual operator in the weighted distributional sense and establish fine properties of the associated function spaces, which in turn allow us to formulate the Poisson problem in an appropriate framework. In light of the close connection between the Poisson problem and its dual problem, we are able to establish various aspects of the theory for the Poisson problem including the solvability, a priori estimates, variants of Kato's inequality and regularity results.

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

CHEN, Huyuan; Konstantinos T. GKIKAS a Phuoc-Tai NGUYEN. Poisson problems involving fractional Hardy operators and measures. Nonlinearity. IOP Publishing Ltd, 2023, roč. 36, č. 12, s. 7191-7229. ISSN 0951-7715. Dostupné z: https://doi.org/10.1088/1361-6544/ad073e.

@article{2364738,
   author = {Chen, Huyuan and Gkikas, Konstantinos T. and Nguyen, PhuocandTai},
   article_number = {12},
   doi = {https://doi.org/10.1088/1361-6544/ad073e},
   keywords = {Poisson problem; fractional hardy Laplacian; Radon measure; Kato's inequality},
   language = {eng},
   issn = {0951-7715},
   journal = {Nonlinearity},
   title = {Poisson problems involving fractional Hardy operators and measures},
   url = {https://iopscience.iop.org/article/10.1088/1361-6544/ad073e},
   volume = {36},
   year = {2023}
}

TY  - JOUR
ID  - 2364738
AU  - Chen, Huyuan - Gkikas, Konstantinos T. - Nguyen, Phuoc-Tai
PY  - 2023
TI  - Poisson problems involving fractional Hardy operators and measures
JF  - Nonlinearity
VL  - 36
IS  - 12
SP  - 7191-7229
EP  - 7191-7229
PB  - IOP Publishing Ltd
SN  - 09517715
KW  - Poisson problem
KW  - fractional hardy Laplacian
KW  - Radon measure
KW  - Kato's inequality
UR  - https://iopscience.iop.org/article/10.1088/1361-6544/ad073e
N2  - In this paper, we study the Poisson problem involving a fractional Hardy operator and a measure source. The complex interplay between the nonlocal nature of the operator, the peculiar effect of the singular potential and the measure source induces several new fundamental difficulties in comparison with the local case. To overcome these difficulties, we perform a careful analysis of the dual operator in the weighted distributional sense and establish fine properties of the associated function spaces, which in turn allow us to formulate the Poisson problem in an appropriate framework. In light of the close connection between the Poisson problem and its dual problem, we are able to establish various aspects of the theory for the Poisson problem including the solvability, a priori estimates, variants of Kato's inequality and regularity results.
ER  -

CHEN, Huyuan; Konstantinos T. GKIKAS a Phuoc-Tai NGUYEN. Poisson problems involving fractional Hardy operators and measures. \textit{Nonlinearity}. IOP Publishing Ltd, 2023, roč.~36, č.~12, s.~7191-7229. ISSN~0951-7715. Dostupné z: https://doi.org/10.1088/1361-6544/ad073e.

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