A Dirichlet Problem for the First Order Inhomogeneous Meta-Monogenic Equation in Parameter Depending Clifford Algebras

被引：1

作者：

Di Teodoro, Antonio ^{[1
]}

Vanegas, Judith ^{[1
]}

机构：

[1] Univ Simon Bolivar, Dept Matemat, Caracas, Venezuela

来源：

COMPLEX ANALYSIS AND OPERATOR THEORY | 2015年 / 9卷 / 05期

关键词：

Dirichlet problem; Clifford-type algebras depending on parameters; Meta-monogenic functions; REPRESENTATION; OPERATOR;

D O I：

10.1007/s11785-014-0390-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Using Clifford-type algebras depending on parameters we solve a Dirichlet problem for the first order inhomogeneous meta-monogenic equation. In order to do that we construct a fundamental solution for first order meta-monogenic operator and give a Cauchy-Pompeiu Formula. Then we reduce the boundary value problem to a fixed-point problem for an integral operator defined using the fundamental solution of the differential operator.

引用

页码：1025 / 1036

页数：12

共 20 条

[1] A Dirichlet Problem for the First Order Inhomogeneous Meta-Monogenic Equation in Parameter Depending Clifford Algebras
Antonio Di Teodoro
Judith Vanegas
[J]. Complex Analysis and Operator Theory, 2015, 9 : 1025 - 1036
[2] Some Integral Representation for Meta-Monogenic Function in Clifford Algebras Depending on Parameters
Cristina Balderrama
Antonio Di Teodoro
Adrian Infante
[J]. Advances in Applied Clifford Algebras, 2013, 23 : 793 - 813
[3] Some Integral Representation for Meta-Monogenic Function in Clifford Algebras Depending on Parameters
Balderrama, Cristina
Di Teodoro, Antonio
Infante, Adrian
[J]. ADVANCES IN APPLIED CLIFFORD ALGEBRAS, 2013, 23 (04) : 793 - 813
[4] A boundary value problem for monogenic functions in parameter-depending Clifford algebras
Tutschke, Wolfgang
Judith Vanegas, Carmen
[J]. COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2011, 56 (1-4) : 113 - 118
[5] First Order Differential Operators Associated to the Space of Monogenic Functions in Parameter-Depending Clifford Algebras
Eusebio Ariza
Judith Vanegas
Franklin Vargas
[J]. Advances in Applied Clifford Algebras, 2016, 26 : 13 - 29
[6] First Order Differential Operators Associated to the Space of Monogenic Functions in Parameter-Depending Clifford Algebras
Ariza, Eusebio
Vanegas, Judith
Vargas, Franklin
[J]. ADVANCES IN APPLIED CLIFFORD ALGEBRAS, 2016, 26 (01) : 13 - 29
[7] Fundamental Solutions for the First Order Meta-Monogenic Operator
Di Teodoro, A. N.
Vanegas, C. J.
[J]. ADVANCES IN APPLIED CLIFFORD ALGEBRAS, 2012, 22 (01) : 49 - 58
[8] Fundamental Solutions for the First Order Meta-Monogenic Operator
A. N. Di Teodoro
C. J. Vanegas
[J]. Advances in Applied Clifford Algebras, 2012, 22 : 49 - 58
[9] Solvability of the Dirichlet problem for an inhomogeneous second-order elliptic equation
Gushchin, A. K.
[J]. SBORNIK MATHEMATICS, 2015, 206 (10) : 1410 - 1439
[10] Approximation to the Dirichlet problem for a higher-order elliptic equation with a spectral parameter and a discontinuous nonlinearity
Potapov, D. K.
[J]. DIFFERENTIAL EQUATIONS, 2007, 43 (07) : 1031 - 1032

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