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Local solvability of a system of equations related to Ricci-flat Kähler metrics. (English) Zbl 1347.35091

Summary: We prove the unique solvability in the holomorphic category of a system of partial differential equations which is a higher order version of the system considered by R. Bielawski [Math. Proc. Camb. Philos. Soc. 132, No. 3, 471–479 (2002; Zbl 1024.53047)] in his study of Ricci-flat Kähler metrics. The system is involves a higher order nonlinear equation that is singular in the variable \(t\) and is very similar to the one studied by R. Gérard and H. Tahara [Singular nonlinear partial differential equations. Wiesbaden: Vieweg (1996; Zbl 0874.35001)] in the 1990s. The proof makes use of a family of majorant functions based on the ones used in [J. E. C. Lope and H. Tahara, J. Math. Pures Appl. (9) 81, No. 9, 811–826 (2002; Zbl 1028.35034)] and [P. Pongérard, J. Math. Sci., Tokyo 7, No. 3, 423–448 (2000; Zbl 0964.35008)].

MSC:

35G55 Initial value problems for systems of nonlinear higher-order PDEs
35A20 Analyticity in context of PDEs
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