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Sbornik: Mathematics, 2001, Volume 192, Issue 10, Pages 1491–1513
DOI: https://doi.org/10.1070/SM2001v192n10ABEH000603 (Mi sm603) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Boundary properties of solutions of equations of minimal surface kind

V. M. Miklyukov

Volgograd State Pedagogical University
English version PDF (246 kB) Citations (3)
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DOI: https://doi.org/10.1070/SM2001v192n10ABEH000603
Abstract: Generalized solutions of equations of minimal-surface type are studied. It is shown that a solution makes at most countably many jumps at the boundary. In particular, a solution defined in the exterior of a disc extends by continuity to the boundary circle everywhere outside a countable point set. An estimate of the sum of certain non-local characteristics of the jumps of a solution at the boundary is presented. A result similar to Fatou's theorem on angular boundary values is proved.
Received: 12.03.2001
Russian version:
Matematicheskii Sbornik, 2001, Volume 192, Number 10, Pages 71–94
DOI: https://doi.org/10.4213/sm603
Bibliographic databases:
UDC: 517.54+517.947
MSC: Primary 53A10, 35J67; Secondary 30C62
Language: English
Original paper language: Russian
Citation: V. M. Miklyukov, “Boundary properties of solutions of equations of minimal surface kind”, Mat. Sb., 192:10 (2001), 71–94; Sb. Math., 192:10 (2001), 1491–1513
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник - 1992–2005 Sbornik: Mathematics
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    English version PDF:7
    References:48
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