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

Masatake 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 -