Medzhidov, Z. G. \(L^2\)-estimates and existence theorems for generalized analytic functions in several variables. (Russian, English) Zbl 1051.32020 Sib. Mat. Zh. 45, No. 4, 843-854 (2004); translation in Sib. Math. J. 45, No. 4, 699-708 (2004). The author considers the generalized Cauchy-Riemann system with nonlinear terms \(\partial u/\partial\overline{z}_j-\overline{a_j u}=f_j\), \(j=1,\dots, n\), in an arbitrary domain of the complex space. Under some natural conditions on the coefficients and compatibility conditions, the author proves solvability of this system in the space of locally square integrable functions. Reviewer: Victor Alexandrov (Novosibirsk) MSC: 32W50 Other partial differential equations of complex analysis in several variables 35N10 Overdetermined systems of PDEs with variable coefficients 32L05 Holomorphic bundles and generalizations Keywords:integrability; compatibility; foliation; Hörmander space PDF BibTeX XML Cite \textit{Z. G. Medzhidov}, Sib. Mat. Zh. 45, No. 4, 843--854 (2004; Zbl 1051.32020); translation in Sib. Math. J. 45, No. 4, 699--708 (2004) Full Text: EMIS EuDML