On the Laplacian vector fields theory in domains with rectifiable boundary

Abstract:

Given a domain Ω in ℝ3 with rectifiable boundary, we consider main integral, and some other, theorems for the theory of Laplacian (sometimes called solenoidal and irrotational, or harmonic) vector fields paying a special attention to the problem of decomposing a continuous vector field, with an additional condition, u on the boundary Γ of Ω ⊂ ℝ3 into a sum u = u+ + u- were u ± are boundary values of vector fields which are Laplacian in Ω and its complement respectively. Our proofs are based on the intimate relations between Laplacian vector fields theory and quaternionic analysis for the Moisil-Theodorescu operator. Copyright © 2006 John Wiley & Sons, Ltd.

Año de publicación:

2006

Keywords:

• Cauchy transform
• Vector fields theory
• Quaternionic analysis

Fuente:

scopus