Geodesic
Dirichlet problems for functions that are harmonic on a two-dimensional net
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences ICMMAS-17, St. Petersburg Polytechnic University, July 24-28, 2017, Tome 160 (2019), pp. 42-48.

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The Dirichlet problem for harmonic functions on a two-dimensional complex of a special type is considered. It is proved that this problem is a Fredholm problem in the Hölder class and its index is zero.
Keywords: two-dimensional complex, Fredholm property, index, Hölder space, harmonic function. 
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L. A. Kovaleva; A. P. Soldatov. Dirichlet problems for functions that are harmonic on a two-dimensional net. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences ICMMAS-17, St. Petersburg Polytechnic University, July 24-28, 2017, Tome 160 (2019), pp. 42-48. http://geodesic.mathdoc.fr/item/INTO_2019_160_a5/

[1] Kovaleva L. A., Soldatov A. P., “Zadacha Dirikhle na dvumernykh stratifitsirovannykh mnozhestvakh”, Izv. RAN. Ser. mat., 79:1 (2015), 77–114 | DOI | MR | Zbl