Electron. J. Differential Equations, Vol. 2017 (2017), No. 51, pp. 1-15.

Solvability of a system of totally characteristic equations related to Kahler metrics

Jose Ernie C. Lope, Mark Philip F. Ona

Abstract:
We consider a system of equations composed of a higher order singular partial differential equation of totally characteristic type and several higher order non-Kowalevskian linear equations. This system is a higher order version of a system that arose in Bielawski's investigations on K\"ahler metrics. We first prove that this system has a unique holomorphic solution. We then show that if the coefficients of the system are in some formal Gevrey class, then the unique solution is also in the same formal Gevrey class.

Submitted October 31, 2016. Published February 21, 2017.
Math Subject Classifications: 35G50, 35A20.
Key Words: Totally characteristic equation; singular partial differential equation; majorant function; formal Gevrey class.

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Jose Ernie C. Lope
Institute of Mathematics, College of Science
University of the Philippines Diliman
Quezon City, Philippines
email: ernie@math.upd.edu.ph
Mark Philip F. Ona
Institute of Mathematics, College of Science
University of the Philippines Diliman
Quezon City, Philippines
email: mpona@math.upd.edu.ph

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