TY - JOUR
T1 - On the Laplacian vector fields theory in domains with rectifiable boundary
AU - Abreu-Blaya, R.
AU - Bory-Reyes, J.
AU - Shapiro, M.
PY - 2006/10
Y1 - 2006/10
N2 - 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.
AB - 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.
KW - Cauchy transform
KW - Quaternionic analysis
KW - Vector fields theory
UR - http://www.scopus.com/inward/record.url?scp=33748874723&partnerID=8YFLogxK
U2 - 10.1002/mma.758
DO - 10.1002/mma.758
M3 - Artículo
SN - 0170-4214
VL - 29
SP - 1861
EP - 1881
JO - Mathematical Methods in the Applied Sciences
JF - Mathematical Methods in the Applied Sciences
IS - 15
ER -