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On the Laplacian vector fields theory in domains with rectifiable boundary

โœ Scribed by R. Abreu-Blaya; J. Bory-Reyes; M. Shapiro

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
195 KB
Volume
29
Category
Article
ISSN
0170-4214

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โœฆ Synopsis

Abstract

Given a domain ฮฉ in โ„^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 ฮ“of ฮฉ โŠ‚ โ„^3^ into a sum u = u^+^+u^โˆ’^ were u^ยฑ^ are boundary values of vector fields which are Laplacian in ฮฉ and its complement respectively. Our proofs are based on the intimate relations between Laplacian vector fields theory and quaternionic analysis for the Moisilโ€“Theodorescu operator. Copyright ยฉ 2006 John Wiley & Sons, Ltd.

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