Geodesic
Series in a Lipschitz perturbation of the boundary for solving the Dirichlet problem
Matematičeskie trudy, Tome 20 (2017) no. 1, pp. 158-200

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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/}
}
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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/