Borel resummation of formal solutions to nonlinear Laplace equations in 2 variables
Annales Polonici Mathematici, Tome 67 (1997) no. 1, pp. 31-41
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We consider a nonlinear Laplace equation Δu = f(x,u) in two variables. Following the methods of B. Braaksma [Br] and J. Ecalle used for some nonlinear ordinary differential equations we construct first a formal power series solution and then we prove the convergence of the series in the same class as the function f in x.
Keywords:
Borel resummation, formal solutions, Laplace equation
Affiliations des auteurs :
M. Pliś 1 ; B. Ziemian 1
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author = {M. Pli\'s and B. Ziemian},
title = {Borel resummation of formal solutions to nonlinear {Laplace} equations in 2 variables},
journal = {Annales Polonici Mathematici},
pages = {31--41},
publisher = {mathdoc},
volume = {67},
number = {1},
year = {1997},
doi = {10.4064/ap-67-1-31-41},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ap-67-1-31-41/}
}
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M. Pliś; B. Ziemian. Borel resummation of formal solutions to nonlinear Laplace equations in 2 variables. Annales Polonici Mathematici, Tome 67 (1997) no. 1, pp. 31-41. doi: 10.4064/ap-67-1-31-41
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