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Sbornik: Mathematics, 1999, Volume 190, Issue 10, Pages 1417–1448
DOI: https://doi.org/10.1070/sm1999v190n10ABEH000431 (Mi sm431) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Existence of boundary values for metaharmonic functions

V. P. Mikhailov

Steklov Mathematical Institute, Russian Academy of Sciences
English version PDF (538 kB) Citations (11)
References:
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DOI: https://doi.org/10.1070/sm1999v190n10ABEH000431
Abstract: Necessary and sufficient conditions for the existence of $L_2$-limits at the boundary of solutions of a metaharmonic equation in a half-space are established. In the case of Laplace's equation these criteria coincide with Riesz's theorem: a harmonic function has an $L_2$-limit at the boundary if and only if it is $L_2$-bounded.
Received: 17.03.1999
Russian version:
Matematicheskii Sbornik, 1999, Volume 190, Number 10, Pages 17–48
DOI: https://doi.org/10.4213/sm431
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 31B30, 35J30, 35J67
Language: English
Original paper language: Russian
Citation: V. P. Mikhailov, “Existence of boundary values for metaharmonic functions”, Mat. Sb., 190:10 (1999), 17–48; Sb. Math., 190:10 (1999), 1417–1448
Citation in format AMSBIB
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    English version PDF:8
    References:78
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