Journal of the Mathematical Society of Japan

Growth property and slowly increasing behaviour of singular solutions of linear partial differential equations in the complex domain

Sunao ŌUCHI

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Abstract

Consider a linear partial differential equation in Cd+1P(z,)u(z)=f(z), where u(z) and f(z) admit singularities on the surface {z0=0}. We assume that |f(z)|A|z0|c in some sectorial region with respect to z0. We can give an exponent γ*>0 for each operator P(z,) and show for those satisfying some conditions that if ϵ>0Cϵ such that |u(z)|Cϵexp(ϵ|z0|-γ*) in the sectorial region, then |u(z)|C|z0|c for some constants c and C.

Article information

Source
J. Math. Soc. Japan, Volume 52, Number 4 (2000), 767-792.

Dates
First available in Project Euclid: 10 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1213107109

Digital Object Identifier
doi:10.2969/jmsj/05240767

Mathematical Reviews number (MathSciNet)
MR1775389

Zentralblatt MATH identifier
0966.35006

Subjects
Primary: 35A20: Analytic methods, singularities
Secondary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 35B40: Asymptotic behavior of solutions

Keywords
Singular solutions complex partial differential equations

Citation

ŌUCHI, Sunao. Growth property and slowly increasing behaviour of singular solutions of linear partial differential equations in the complex domain. J. Math. Soc. Japan 52 (2000), no. 4, 767--792. doi:10.2969/jmsj/05240767. https://projecteuclid.org/euclid.jmsj/1213107109


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