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JOURNALS // Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory // Archive
Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 2019 Volume 160, Pages 42–48 (Mi into423)
Dirichlet problems for functions that are harmonic on a two-dimensional net

L. A. Kovalevaa, A. P. Soldatovbc

a Federal State Public Educational Establishment of Higher Training «Belgorod Law Institute of Ministry of the Internal of the Russian Federation named after I.D. Putilin»
b Dorodnitsyn Computing Centre of the Russian Academy of Sciences, Moscow
c Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Moscow

Abstract: 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.

UDC: 517.9

MSC: 35J05, 35J25



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