# Convergence of formal solutions of first order singular partial differential equations of nilpotent type

Banach Center Publications (2012)

- Volume: 97, Issue: 1, page 91-99
- ISSN: 0137-6934

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topMasatake Miyake, and Akira Shirai. "Convergence of formal solutions of first order singular partial differential equations of nilpotent type." Banach Center Publications 97.1 (2012): 91-99. <http://eudml.org/doc/281602>.

@article{MasatakeMiyake2012,

abstract = {Let (x,y,z) ∈ ℂ³. In this paper we shall study the solvability of singular first order partial differential equations of nilpotent type by the following typical example:
$Pu(x,y,z): = (y∂_x - z∂_y)u(x,y,z) = f(x,y,z) ∈ _\{x,y,z\}$,
where
$P = y∂_x - z∂_y: _\{x,y,z\} → _\{x,y,z\}$.
For this equation, our aim is to characterize the solvability on $_\{x,y,z\}$ by using the Im P, Coker P and Ker P, and we give the exact forms of these sets.},

author = {Masatake Miyake, Akira Shirai},

journal = {Banach Center Publications},

keywords = {nilpotent vector field},

language = {eng},

number = {1},

pages = {91-99},

title = {Convergence of formal solutions of first order singular partial differential equations of nilpotent type},

url = {http://eudml.org/doc/281602},

volume = {97},

year = {2012},

}

TY - JOUR

AU - Masatake Miyake

AU - Akira Shirai

TI - Convergence of formal solutions of first order singular partial differential equations of nilpotent type

JO - Banach Center Publications

PY - 2012

VL - 97

IS - 1

SP - 91

EP - 99

AB - Let (x,y,z) ∈ ℂ³. In this paper we shall study the solvability of singular first order partial differential equations of nilpotent type by the following typical example:
$Pu(x,y,z): = (y∂_x - z∂_y)u(x,y,z) = f(x,y,z) ∈ _{x,y,z}$,
where
$P = y∂_x - z∂_y: _{x,y,z} → _{x,y,z}$.
For this equation, our aim is to characterize the solvability on $_{x,y,z}$ by using the Im P, Coker P and Ker P, and we give the exact forms of these sets.

LA - eng

KW - nilpotent vector field

UR - http://eudml.org/doc/281602

ER -

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