Series in a Lipschitz perturbation of the boundary for solving the Dirichlet problem
Matematičeskie trudy, Tome 20 (2017) no. 1, pp. 158-200
Voir la notice de l'article provenant de la source Math-Net.Ru
In a special Lipschitz domain treated as a perturbation of the upper
half-space,
we construct a perturbation theory series for a positive harmonic function
with zero trace.
The terms of the series are harmonic extensions to the half-space
from its boundary of distributions defined by a recurrent formula and passage
to the limit.
The approximation error by a segment of the series is estimated
via a power of the seminorm of the perturbation
in the homogeneous Slobodestkiĭ
space $b_N^{1-1/N}$. The series converges if the Lipschitz constant
of the perturbation is small.
@article{MT_2017_20_1_a9,
author = {A. I. Parfenov},
title = {Series in a {Lipschitz} perturbation of the boundary for solving the {Dirichlet} problem},
journal = {Matemati\v{c}eskie trudy},
pages = {158--200},
publisher = {mathdoc},
volume = {20},
number = {1},
year = {2017},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MT_2017_20_1_a9/}
}
A. I. Parfenov. Series in a Lipschitz perturbation of the boundary for solving the Dirichlet problem. Matematičeskie trudy, Tome 20 (2017) no. 1, pp. 158-200. http://geodesic.mathdoc.fr/item/MT_2017_20_1_a9/