Higher Order Dirichlet-Type Problems in 2D Complex Quaternionic Analysis
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F19%3AA20021T3" target="_blank" >RIV/61988987:17310/19:A20021T3 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1134/S1063454119040083" target="_blank" >https://link.springer.com/article/10.1134/S1063454119040083</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1134/S1063454119040083" target="_blank" >10.1134/S1063454119040083</a>
Alternative languages
Result language
angličtina
Original language name
Higher Order Dirichlet-Type Problems in 2D Complex Quaternionic Analysis
Original language description
It is well known that developing methods for solving Dirichlet problems is important and relevant for various areas of mathematical physics related to the Laplace equation, the Helmholtz equation, the Stokes equation, the Maxwell equation, the Dirac equation, and others. The author in previous papers studied the solvability of Dirichlet boundary value problems of the first and second orders in quaternionic analysis. In the present paper, we study a higher-order Dirichlet boundary value problem associated with the two-dimensional Helmholtz equation with complex potential. The exis- tence and uniqueness of a solution to the Dirichlet boundary value problem in the two-dimensional case is proved and an appropriate representation formula for the solution of this problem is found. Most Dirichlet problems are solved for the case in three variables. Note that the case of two variables is not a simple consequence of the three-dimensional case. To solve the problem, we use the method of orthogonal decomposition of the quaternion-valued Sobolev space. This orthogonal decomposi- tion of the space is also a tool for the study of many elliptic boundary value problems that arise in var- ious areas of mathematics and mathematical physics. An orthogonal decomposition of the quater- nion-valued Sobolev space with respect to the high-order Dirac operator is also obtained in this paper.
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
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Vestnik St. Petersburg University, Mathematics
ISSN
1063-4541
e-ISSN
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Volume of the periodical
52
Issue of the periodical within the volume
4
Country of publishing house
RU - RUSSIAN FEDERATION
Number of pages
12
Pages from-to
646-658
UT code for WoS article
000511668500010
EID of the result in the Scopus database
2-s2.0-85077032591