## Boundary behaviour of the complex Monge-Ampère equation.(English)Zbl 0496.35042

### MSC:

 35J70 Degenerate elliptic equations 32T99 Pseudoconvex domains 58J99 Partial differential equations on manifolds; differential operators

### Citations:

Zbl 0362.53049; Zbl 0322.32012
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### References:

 [1] Cheng, S.-Y. &Yau, S. T., On the existence of a complete Kähler metric on non-compact complex manifolds and the regularity of Fefferman’s equation.Comm. Pure Appl. Math., 33 (1980), 507–544. · Zbl 0506.53031 [2] Fefferman, C., Monge-Ampère equations, the Bergman kernel and geometry of pseudoconvex domains.Ann. of Math., 103 (1976), 395–416. · Zbl 0322.32012 [3] Greiner, P. C. &Stein, E. M., Estimates for the $$\bar \partial$$ Problem. Mathematical Notes no. 19, Princeton University Press, Princeton N.J., 1977. · Zbl 0354.35002 [4] Melrose, R. B., Transformation of boundary problems.Acta Math., 147: 3–4 (1981), 149–236. · Zbl 0492.58023 [5] Yau, S. T., On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation I.Comm. Pure Appl. Math., 31 (1978), 339–411. · Zbl 0369.53059 [6] Graham, C. R.,The Dirichlet problem for the Bergman Laplacian. Thesis, Princeton University, 1981.
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