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

Antonio Di Teodoro; Judith Vanegas

doi:10.1007/s11785-014-0390-2

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

Antonio Di Teodoro^*
, Judith Vanegas

^*Corresponding author for this work

Universidad Simón Bolívar

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	1025-1036
Number of pages	12
Journal	Complex Analysis and Operator Theory
Volume	9
Issue number	5
DOIs	https://doi.org/10.1007/s11785-014-0390-2
State	Published - 18 Jun 2015
Externally published	Yes

Keywords

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

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10.1007/s11785-014-0390-2

Cite this

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abstract = "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.",

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AU - Di Teodoro, Antonio

AU - Vanegas, Judith

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N2 - 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.

AB - 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.

KW - Clifford-type algebras depending on parameters

KW - Dirichlet problem

KW - Meta-monogenic functions

UR - https://www.scopus.com/pages/publications/84939897407

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DO - 10.1007/s11785-014-0390-2

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SN - 1661-8254

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ER -

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

Abstract

Keywords

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