L2-Estimates and Existence Theorems for Generalized Analytic Functions in Several Variables
- 23 Downloads
We consider the generalized Cauchy–Riemann system with nonlinear terms in an arbitrary domain of the complex space. Under some natural conditions on the coefficients and compatibility conditions, we prove solvability of this system in the space of locally square integrable functions.
Unable to display preview. Download preview PDF.
- 1.Magomedov G. A. and Palamodov V. P., “Generalized analytic functions in several variables,” Mat. Sb., 106, No. 4, 515–543 (1978).Google Scholar
- 2.Vekua I. N., Generalized Analytic Functions [in Russian], Nauka, Moscow (1988).Google Scholar
- 3.Koohara A., “Similarity principle of the generalized Cauchy-Riemann equations for several complex variables,” J. Math. Soc. Japan., 23, 213–249 (1971).Google Scholar
- 4.Mikha?ilov L. G. and Abrosimov A. V., “On some overdetermined systems of partial differential equations,” Dokl. Akad. Nauk Tadzhik. SSR, 14, No. 6, 9–13 (1971).Google Scholar
- 5.Mikha?ilov L. G. and Abrosimov A. V., “The Cauchy-Riemann generalized system in several independent variables,” Dokl. Akad. Nauk SSSR, 210, No. 1, 26–29 (1973).Google Scholar
- 6.Mikha?ilov L. G., “On compatibility conditions and solution set of the Cauchy-Riemann generalized system in several variables,” Dokl. Akad. Nauk SSSR, 249, No. 6, 1313–1317 (1979).Google Scholar
- 7.Hörmander L., An Introduction to Complex Analysis in Several Variables [Russian translation], Mir, Moscow (1968).Google Scholar
- 8.Hörmander L., “L2-Estimates and existence theorems for an operator \(\overline \partial \),” Matematika, 10, No. 2, 59–116 (1966).Google Scholar
- 9.Chern Shiing-shen, Complex Manifolds [Russian translation], Izdat. Inostr. Lit., Moscow (1961). 708Google Scholar