# Borel resummation of formal solutions to nonlinear Laplace equations in 2 variables

Annales Polonici Mathematici (1997)

- Volume: 67, Issue: 1, page 31-41
- ISSN: 0066-2216

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topM. E. Pliś, and B. Ziemian. "Borel resummation of formal solutions to nonlinear Laplace equations in 2 variables." Annales Polonici Mathematici 67.1 (1997): 31-41. <http://eudml.org/doc/270185>.

@article{M1997,

abstract = {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.},

author = {M. E. Pliś, B. Ziemian},

journal = {Annales Polonici Mathematici},

keywords = {Borel resummation; formal solutions; Laplace equation; Laplace transform; formal power series solution},

language = {eng},

number = {1},

pages = {31-41},

title = {Borel resummation of formal solutions to nonlinear Laplace equations in 2 variables},

url = {http://eudml.org/doc/270185},

volume = {67},

year = {1997},

}

TY - JOUR

AU - M. E. Pliś

AU - B. Ziemian

TI - Borel resummation of formal solutions to nonlinear Laplace equations in 2 variables

JO - Annales Polonici Mathematici

PY - 1997

VL - 67

IS - 1

SP - 31

EP - 41

AB - 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.

LA - eng

KW - Borel resummation; formal solutions; Laplace equation; Laplace transform; formal power series solution

UR - http://eudml.org/doc/270185

ER -

## References

top- [Br] B. Braaksma, Multisummability of formal power series solutions of nonlinear meromorphic differential equations, Ann. Inst. Fourier (Grenoble) 42 (1992), 517-541. Zbl0759.34003
- [Sz-Zie] Z. Szmydt and B. Ziemian, The Mellin Transformation and Fuchsian Type PDEs, Kluwer, 1992. Zbl0771.35002
- [Zie1] B. Ziemian, Generalized analytic functions with applications to singular ordinary and partial differential equations, Dissertationes Math. 354 (1996).
- [Zie2] B. Ziemian, Leray residue formula and asymptotics of solutions to constant coefficient PDEs, Topol. Methods Nonlinear Anal. 3 (1994), 257-293. Zbl0813.47060

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