The Dirichlet problem for a complex Monge-Ampère equation. (English) Zbl 0315.31007


31C10 Pluriharmonic and plurisubharmonic functions
35Q99 Partial differential equations of mathematical physics and other areas of application
35J25 Boundary value problems for second-order elliptic equations
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[1] Alexandrov, A. D.: The Dirichlet problem for the equation Det ?z i,j ?=?(z 1,...,z n ,x 1,...,x n ), I. Vestnik, Leningrad Univ.13, No. 1, 5-24 (1958)
[2] Bergman, S.: Functions of extended class in the theory of functions of several complex variables. Trans. Amer. Math. Soc.63, 523-547 (1948) · Zbl 0034.05304 · doi:10.1090/S0002-9947-1948-0025583-9
[3] Bergman, S.: Kernel functions and extended classes in the theory of functions of complex variables, Colloque sur les fonctions de plusieur variables. Bruxelles pp. 135-157 (1953)
[4] Bremermann, H.: On a generalized Dirichlet problem for plurisubharmonic functions and pseudoconvex domains. Characterization of Silov boundaries. Trans. Amer. Math. Soc.91, 246-276 (1959) · Zbl 0091.07501
[5] Cheng, S.-Y., Yau, S.-T.: Complete affine hypersurfaces, Parts I, II, III. To appear
[6] Chern, S. S., Levine, Harold I., Nirenberg, L.: Intrinsic norms on a complex manifold. Global Analysis (Papers in honor of K. Kodaira), pp. 119-139 Tokyo: Univ. of Tokyo Press 1969 · Zbl 0202.11603
[7] Chern, S. S., Moser, J.: Real hypersurfaces in complex manifolds. Acta Math.133, 219-271 (1974) · Zbl 0302.32015 · doi:10.1007/BF02392146
[8] Christoffers, H.: Princeton University Thesis, to appear
[9] Diederich, K.: Über die 1. und 2. Ableitungen der Bergmannschen Kernfunktion und ihr Randverhalten. Math. Ann.203, 129-170 (1963) · Zbl 0253.32011 · doi:10.1007/BF01431441
[10] Fefferman, C.: Monge-Ampere equations, the Bergman Kernel, and geometry of pseudoconvex domains. Ann. of Math.,103, 395-416 (1976) · Zbl 0322.32012 · doi:10.2307/1970945
[11] Gluck, H.: Manifolds with preassigned curvature?a survey. Bull. Amer. Math. Soc.81, 313-329 (1975) · Zbl 0299.53025 · doi:10.1090/S0002-9904-1975-13740-2
[12] Goffman, C., Serrin, J.: Sublinear functions of measures and variational integrals. Duke Math. J.31, 159-178 (1964) · Zbl 0123.09804 · doi:10.1215/S0012-7094-64-03115-1
[13] Hörmander, L.: Complex analysis in several variables. New York: North Holland/American Elsevier 1973 · Zbl 0271.32001
[14] Hörmander, L.:L 2 estimates and existence theorems for the ? operator. Acta Math.113, 89-152 (1965) · Zbl 0158.11002 · doi:10.1007/BF02391775
[15] Kerzman, N., Kohn, J.J., Nirenberg, L.: Lecture at Amer. Math. Soc. Conference on Several Complex Variables. Williamstown, Mass, August, 1975
[16] Koppelman, W.: The Cauchy integral formula for functions of several complex variables, Bull. Amer. Math. Soc.73, 373-377 (1967) · Zbl 0177.11103 · doi:10.1090/S0002-9904-1967-11757-9
[17] Lelong, P.: Plurisubharmonic functions and positive differential forms, New York: Gordon and Breach 1969 · Zbl 0195.11604
[18] Pelles, D. A.: Intrinsic measures on complex manifolds and holomorphic mappings. Amer. Math. Soc. Memoir Number96, 1970
[19] Pogorelov, A. V.: Monge-Ampere equations of elliptic type. Groningen: Noordhoff 1964 · Zbl 0133.04902
[20] Pogorelov, A. V.: The Dirichlet problem for then-dimensional analogue of the Monge-Ampere equation, Soviet Math. Dokl.12, 1727-1731 (1971) · Zbl 0238.35071
[21] Rudin, W.: Real and complex analysis. New York: McGraw Hill 1974 · Zbl 0278.26001
[22] Siu, Y. T.: Extension of meromorphic maps. Ann. of Math.102, 421-462 (1975) · Zbl 0318.32007 · doi:10.2307/1971038
[23] Walsh, J. B.: Continuity of envelopes of plurisubharmonic functions. J. Math. Mech.18, 143-148 (1968) · Zbl 0159.16002
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