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\(L^2\)-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.
32W50 Other partial differential equations of complex analysis in several variables
35N10 Overdetermined systems of PDEs with variable coefficients
32L05 Holomorphic bundles and generalizations
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