Higher Order Dirichlet-Type Problems in 2D Complex Quaternionic Analysis

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Higher Order Dirichlet-Type Problems in 2D Complex Quaternionic Analysis

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Higher Order Dirichlet-Type Problems in 2D Complex Quaternionic Analysis

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Vestnik St. Petersburg University, Mathematics

ISSN

1063-4541

e-ISSN

—

Svazek periodika

52

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

RU - Ruská federace

Počet stran výsledku

12

Strana od-do

646-658

Kód UT WoS článku

000511668500010

EID výsledku v databázi Scopus

2-s2.0-85077032591