Analytic continuation and domains of holomorphy for solution to the complex Laplace and Dirac equations in $\bold C^n$ are studied. First, geometric description of envelopes of holomorphy over domains in $\bold E^n$ is given. In more general case, solutions can be continued by integral formulas using values on a real $n-1$ dimensional cycle in $\bold C^n$. Sufficient conditions for this being possible are formulated.
@article{118429,
author = {Martin Kol\'a\v r},
title = {Envelopes of holomorphy for solutions of the Laplace and Dirac equations},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {32},
year = {1991},
pages = {479-494},
zbl = {0759.32008},
mrnumber = {1159796},
language = {en},
url = {http://dml.mathdoc.fr/item/118429}
}
Kolář, Martin. Envelopes of holomorphy for solutions of the Laplace and Dirac equations. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) pp. 479-494. http://gdmltest.u-ga.fr/item/118429/
Clifford Analysis, Research Notes in Mathematics No.76, Pitman 1982. | Zbl 1058.30043
Generalized hypercomplex analysis and its integral formulas, Complex Variables: Theory and Application 5 (1985), 53-70. (1985) | MR 0822855
Leray residues applied to the solution of the Laplace and Wave equations, Seminari di geometria, Bologna (1984), 93-107. (1984) | MR 0866151
Cells of harmonicity and generalized Cauchy integral formula, Proc. London Math. Society (3) 60 (1990), 295-318. (1990) | MR 1031455
Holomorphic continuation of harmonic functions, Ann. Polon. Math. 29 (1974), 67-73. (1974) | MR 0352530 | Zbl 0247.32011