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Izvestiya: Mathematics, 2015, Volume 79, Issue 1, Pages 74–108
DOI: https://doi.org/10.1070/IM2015v079n01ABEH002735 (Mi im8223) 		 
This article is cited in 3 scientific papers (total in 3 papers)

The Dirichlet problem on two-dimensional stratified sets

L. A. Kovaleva, A. P. Soldatov

National Research University "Belgorod State University"
English version PDF (506 kB) Citations (3)
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DOI: https://doi.org/10.1070/IM2015v079n01ABEH002735
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 0113РК01031
This paper was written with the support of the International Project (0113RK01031) of the Ministry of Science and Education of the Republic of Kazakhstan.
Received: 14.02.2014
Revised: 24.03.2014
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2015, Volume 79, Issue 1, Pages 77–114
DOI: https://doi.org/10.4213/im8223
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 30E25, 31A20
Language: English
Original paper language: Russian
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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  • https://www.mathnet.ru/eng/im/v79/i1/p77
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:618
    Russian version PDF:200
    English version PDF:21
    References:119
    First page:54
     
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