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Izv. RAN. Ser. Mat., 2015, Volume 79, Issue 1, Pages 77–114 (Mi izv8223)  

This article is cited in 2 scientific papers (total in 2 papers)

The Dirichlet problem on two-dimensional stratified sets

L. A. Kovaleva, A. P. Soldatov

National Research University "Belgorod State University"

Abstract: We consider the Dirichlet problem for harmonic functions on two-dimensional stratified sets, which are assumed for simplicity to be complexes. We show that under certain conditions this problem is Fredholm in the Hölder space and in weighted Hölder spaces of functions satisfying the Hölder condition outside any neighbourhood of the vertex set of the complex and admitting power singularities. We also study the power-logarithmic asymptotics of solutions at these vertices.

Keywords: Dirichlet problem, two-dimensional complex, harmonic functions, Fredholm property, index, end symbol, weighted Hölder space, power-logarithmic asymptotics.

Funding Agency Grant Number
Ministry of Education and Science of the Republic of Kazakhstan 011301031
This paper was written with the support of the International Project (0113RK01031) of the Ministry of Science and Education of the Republic of Kazakhstan.


DOI: https://doi.org/10.4213/im8223

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English version:
Izvestiya: Mathematics, 2015, 79:1, 74–108

Bibliographic databases:

UDC: 517.9
MSC: 30E25, 31A20
Received: 14.02.2014
Revised: 24.03.2014

Citation: L. A. Kovaleva, A. P. Soldatov, “The Dirichlet problem on two-dimensional stratified sets”, Izv. RAN. Ser. Mat., 79:1 (2015), 77–114; Izv. Math., 79:1 (2015), 74–108

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. Andreyev A.A., Padchenko V.P., Kozlova E.A., “To the 70Th Anniversary of Professor Alexander Pavlovich Soldatov”, Vestn. Samar. Gos. Tekhnicheskogo Univ.-Ser. Fiz.-Mat. Nauka, 22:1 (2018), 15–22  crossref  isi
    2. L. A. Kovaleva, A. P. Soldatov, “Zadacha Dirikhle dlya funktsii, garmonicheskikh na dvumernoi seti”, Materialy mezhdunarodnoi konferentsii«InternationalConference onMathematicalModellinginAppliedSciences, ICMMAS-17», Sankt-Peterburgskii politekhnicheskii universitet,2428 iyulya2017 g., Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 160, VINITI RAN, M., 2019, 42–48  mathnet  mathscinet
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