Green's formulas and Poisson's equation for bosonic Laplacians
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F24%3A00139293" target="_blank" >RIV/00216224:14310/24:00139293 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1002/mma.6922" target="_blank" >https://doi.org/10.1002/mma.6922</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/mma.6922" target="_blank" >10.1002/mma.6922</a>
Alternative languages
Result language
angličtina
Original language name
Green's formulas and Poisson's equation for bosonic Laplacians
Original language description
A bosonic Laplacian is a conformally invariant second-order differential operator acting on smooth functions defined on domains in Euclidean space and taking values in higher-order irreducible representations of the special orthogonal group. In this paper, we firstly introduce the motivation for study of the generalized Maxwell operators and bosonic Laplacians (also known as the higher spin Laplace operators). Then, with the help of connections between Rarita-Schwinger type operators and bosonic Laplacians, we solve Poisson's equation for bosonic Laplacians. A representation formula for bounded solutions to Poisson's equation in Euclidean space is also provided. In the end, we provide Green's formulas for bosonic Laplacians in scalar-valued and Clifford-valued cases, respectively. These formulas reveal that bosonic Laplacians are self-adjoint with respect to a givenL(2)inner product on certain compact supported function spaces.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GJ19-14413Y" target="_blank" >GJ19-14413Y: Linear and nonlinear elliptic equations with singular data and related problems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematical Methods in the Applied Sciences
ISSN
0170-4214
e-ISSN
1099-1476
Volume of the periodical
47
Issue of the periodical within the volume
10
Country of publishing house
US - UNITED STATES
Number of pages
12
Pages from-to
7850-7861
UT code for WoS article
000573339100001
EID of the result in the Scopus database
2-s2.0-85091610587