Poisson problems involving fractional Hardy operators and measures

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F23%3A00134388" target="_blank" >RIV/00216224:14310/23:00134388 - isvavai.cz</a>

Výsledek na webu

<a href="https://iopscience.iop.org/article/10.1088/1361-6544/ad073e" target="_blank" >https://iopscience.iop.org/article/10.1088/1361-6544/ad073e</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/1361-6544/ad073e" target="_blank" >10.1088/1361-6544/ad073e</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Poisson problems involving fractional Hardy operators and measures

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Poisson problems involving fractional Hardy operators and measures

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA22-17403S" target="_blank" >GA22-17403S: Nelineární Schrödingerovy rovnice a systémy se singulárním potenciálem</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Nonlinearity

ISSN

0951-7715

e-ISSN

1361-6544

Svazek periodika

36

Číslo periodika v rámci svazku

12

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

39

Strana od-do

7191-7229

Kód UT WoS článku

001121135200001

EID výsledku v databázi Scopus

2-s2.0-85177781847