We consider a linear partial differential equation with holomorphic coefficients in a neighbourhood of
z=0 in
Cd+1,
P(
z, ∂)
u(
z)=
f(
z),
where
u(
z) and
f(
z) admit singularities on the surface
K={
z0=0}. Our main result is the following:
For the operator
P we define an exponent γ
* called the minimal irregularity of
K and show that if
u(
z) grows at most exponentially with exponent γ
* as
z0 tends to 0 and if
f(
z) has a Gevrey type expansion of exponent γ
* with respect to
z0, then
u(
z) also has the same one.
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