On Weighted Dirac Operators and Their Fundamental Solutions for Anisotropic Media

被引：9

作者：

Vanegas, Judith ^{[1
]}

Vargas, Franklin ^{[2
]}

机构：

[1] Univ Simon Bolivar, Dept Matemat Puras & Aplicadas, Apartado Postal 89000, Caracas, Venezuela

[2] Univ Simon Bolivar, Dept Comp Cient & Estadist, Apartado Postal 89000, Caracas, Venezuela

来源：

ADVANCES IN APPLIED CLIFFORD ALGEBRAS | 2018年 / 28卷 / 02期

关键词：

Second-order elliptic equations; Fundamental solutions; Clifford algebras depending on parameters;

D O I：

10.1007/s00006-018-0860-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The heat transfer problem in isotropic media has been studied extensively in Clifford analysis, but very little in the anisotropic case for this setting. As a first step in this way, we introduce in this work Dirac operators with weights belonging to the Clifford algebra A(n), which factor the second order elliptic differential operator (Delta) over tilde (n) = div(B del), where B is an element of R-nxn is a symmetric and positive definite matrix. For these weighted Dirac operators we construct fundamental solutions and get a Borel-Pompeiu and Cauchy integral formula.

引用

页数：13

共 16 条

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