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Separately analytic functions, generalizations of Hartogs' theorem, and envelopes of holomorphy
Sbornik. Mathematics, Tome 30 (1976) no. 1, pp. 51-67 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $\mathscr D$ and $\mathcal G$ be arbitrary Stein manifolds, $E\subset\mathscr D$ and $F\subset\mathscr G$ compact sets, and $X=(E\times\mathscr G)\cup(\mathscr D\times F)$. Under certain general hypotheses it is proved that a function $f$ on $X$ which is separately analytic, i.e. for which $f(z,w)$ is analytic in $z$ in $\mathscr D$ for any fixed $w\in F$ and analytic in $w$ in $\mathscr G$ for any fixed $z\in E$, extends to an analytic function in some open neighborhood $\widetilde X$ of $X$ which is the envelope of holomorphy of $X$. The envelope of holomorphy of $X$ is studied in those cases in which $X$ has no open envelope of holomorphy. Bibliography: 26 titles. 
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V. P. Zaharyuta. Separately analytic functions, generalizations of Hartogs' theorem, and envelopes of holomorphy. Sbornik. Mathematics, Tome 30 (1976) no. 1, pp. 51-67. http://geodesic.mathdoc.fr/item/SM_1976_30_1_a3/

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