MR
Jose Ernie C. LOPE and Mark Philip F. ONA
Jose Ernie C. LOPE and Mark Philip F. ONA
Local Solvability of a System of Equations Related to Ricci-Flat Kähler Metrics
Funkcialaj Ekvacioj. Serio Internacia
59
2016
141--155
http://fe.math.kobe-u.ac.jp/FE/FullPapers/59-1/59_141.pdf
http://www.ams.org/mathscinet-getitem?mr=MR
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 Bielawski [1] 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 Gérard and Tahara [3] in the 1990s. The proof makes use of a family of majorant functions based on the ones used in Lope-Tahara [6] and Pongérard [4].
Ricci-flat Kähler metrics, Singular Cauchy problem, Majorant functions.
35G50, 35A20.
59-141
2016
Local Solvability of a System of Equations Related to Ricci-Flat Kähler Metrics
Jose Ernie C. LOPE and Mark Philip F. ONA
Jose Ernie C. LOPE and Mark Philip F. ONA
1
Bielawski, R.
Ricci-flat Kähler metrics on canonical bundles
Math. Proc. Cambridge Philos. Soc.
132
2002
471-479
MR1891684
2
Gérard, R.; Tahara, H.
Holomorphic and singular solutions of nonlinear singular first order partial differential equations
Publ. Res. Inst. Math. Sci.
26
1990
979-1000
MR1079905
3
Gérard, R.; Tahara, H.
Singular nonlinear partial differential equations
Aspects of Mathematics, Friedr. Vieweg & Sohn, Braunschweig
1996
MR1757086
4
Pongérard, P.
Sur une Classe d'Équations de Fuchs non Linéaires
J. Math. Sci. Univ. Tokyo
7
2000
423-448
MR1792735
5
Lax, P. D.
Nonlinear hyperbolic equations
Comm. Pure Appl. Math.
6
1953
231-258
MR0056176
6
Lope, J. E. C.; Tahara, H.
On the analytic continuation of solutions to nonlinear partial differential equations
J. Math. Pures Appl. (9)
81
2002
811-826
MR1940368