Singular Solutions with Asymptotic Expansion of Linear Partial Differential Equations in the Complex Domain

  • Sunao Ōuchi

    Sophia University, Tokyo, Japan

Abstract

We consider a linear partial differential equation with holomorphic coefficients in a neighbourhood of in ,

where and admit singularities on the surface . Our main result is the following:

For the operator we define an exponent called the minimal irregularity of and show that if grows at most exponentially with exponent as tends to and if has a Gevrey type expansion of exponent with respect to , then also has the same one.

Cite this article

Sunao Ōuchi, Singular Solutions with Asymptotic Expansion of Linear Partial Differential Equations in the Complex Domain. Publ. Res. Inst. Math. Sci. 34 (1998), no. 4, pp. 291–311

DOI 10.2977/PRIMS/1195144627