For functions that are separately solutions of an elliptic homogeneous PDE with constant coefficients, we prove an analogue of Siciak's theorem for separately holomorphic functions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap80-0-17, author = {Nguyen Thanh Van}, title = {Analytic continuation for some classes of separately analytic functions of real variables}, journal = {Annales Polonici Mathematici}, volume = {81}, year = {2003}, pages = {203-209}, zbl = {1032.31003}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap80-0-17} }
Nguyen Thanh Van. Analytic continuation for some classes of separately analytic functions of real variables. Annales Polonici Mathematici, Tome 81 (2003) pp. 203-209. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap80-0-17/