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The Dirichlet problem for a complex Monge-Ampère equation. (English) Zbl 0322.31008

MSC:
31C10 Pluriharmonic and plurisubharmonic functions
32U05 Plurisubharmonic functions and generalizations
35Q99 Partial differential equations of mathematical physics and other areas of application
32D05 Domains of holomorphy
35J25 Boundary value problems for second-order elliptic equations
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References:
[1] A. D. Aleksandrov, Dirichlet’s problem for the equation \?\?\?||\?\?\?||=\?(\?\(_{1}\),\cdots,\?_\?,\?,\?\(_{1}\),\cdots,\?_\?). I, Vestnik Leningrad. Univ. Ser. Mat. Meh. Astr. 13 (1958), no. 1, 5 – 24 (Russian, with English summary). · Zbl 0114.30202
[2] H. J. Bremermann, On a generalized Dirichlet problem for plurisubharmonic functions and pseudo-convex domains. Characterization of Šilov boundaries, Trans. Amer. Math. Soc. 91 (1959), 246 – 276. · Zbl 0091.07501
[3] S. S. Chern, Harold I. Levine, and Louis Nirenberg, Intrinsic norms on a complex manifold, Global Analysis (Papers in Honor of K. Kodaira), Univ. Tokyo Press, Tokyo, 1969, pp. 119 – 139. · Zbl 0202.11603
[4] P. Lelong, Fonctions plurisousharmoniques et formes différentielles positives, Gordon & Breach, Paris-London-New York (Distributed by Dunod éditeur, Paris), 1968 (French). · Zbl 0192.20103
[5] A. V. Pogorelov, Monge-Ampère equations of elliptic type, Translated from the first Russian edition by Leo F. Boron with the assistance of Albert L. Rabenstein and Richard C. Bollinger, P. Noordhoff, Ltd., Groningen, 1964. · Zbl 0133.04902
[6] A. V. Pogorelov, The Dirichlet problem for the multidimensional analogue of the Monge-Ampère equation, Dokl. Akad. Nauk SSSR 201 (1971), 790 – 793 (Russian).
[7] Y. T. Siu, Extension of meromorphic maps, Ann. of Math. (to appear). · Zbl 0318.32007
[8] J. B. Walsh, Continuity of envelopes of plurisubharmonic functions, J. Math. Mech. 18 (1968/1969), 143 – 148. · Zbl 0159.16002
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