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On the Laplacian vector fields theory in domains with rectifiable boundary
Author(s) -
AbreuBlaya R.,
BoryReyes J.,
Shapiro M.
Publication year - 2006
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.758
Subject(s) - solenoidal vector field , mathematics , vector field , conservative vector field , laplace operator , vector laplacian , boundary (topology) , mathematical proof , mathematical analysis , potential theory , vector operator , operator (biology) , vector potential , domain (mathematical analysis) , complement (music) , pure mathematics , field (mathematics) , geometry , physics , repressor , chemistry , biochemistry , quantum mechanics , magnetic field , compressibility , transcription factor , thermodynamics , complementation , gene , phenotype
Given a domain Ω in ℝ 3 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 Γof Ω ⊂ ℝ 3 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.
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