A family of fundamental solutions of elliptic partial differential operators with quaternion constant coefficients

被引：11

作者：

Dalla Riva, M. ^{[1
]}

Morais, J. ^{[1
]}

Musolino, P. ^{[2
]}

机构：

[1] Univ Aveiro, CIDMA, P-3810193 Aveiro, Portugal

[2] Univ Rennes 1, Inst Rech Math Rennes IRMAR, F-35042 Rennes, France

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2013年 / 36卷 / 12期

关键词：

fundamental solutions; quaternion analysis; elliptic partial differential operators with quaternion constant coefficients; layer potentials; BOUNDARY INTEGRAL-OPERATORS; DERIVATIVES;

D O I：

10.1002/mma.2706

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this paper is to construct a family of fundamental solutions for elliptic partial differential operators with quaternion constant coefficients. The elements of such family are expressed by means of functions, which depend jointly real analytically on the coefficients of the operators and on the spatial variable. We show some regularity properties in the frame of Schauder spaces for the corresponding single layer potentials. Ultimately, we exploit our construction by showing a real analyticity result for perturbations of the layer potentials corresponding to complex elliptic partial differential operators of order two. Copyright (c) 2012 John Wiley & Sons, Ltd.

引用

页码：1569 / 1582

页数：14

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