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.
\Bibitem{Mik01}
\by V.~M.~Miklyukov
\paper Boundary properties of solutions of equations of minimal surface kind
\jour Sb. Math.
\yr 2001
\vol 192
\issue 10
\pages 1491--1513
\mathnet{http://mi.mathnet.ru/eng/sm603}
\crossref{https://doi.org/10.1070/SM2001v192n10ABEH000603}
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Linking options:
https://www.mathnet.ru/eng/sm603
https://doi.org/10.1070/SM2001v192n10ABEH000603
https://www.mathnet.ru/eng/sm/v192/i10/p71
This publication is cited in the following 3 articles:
A. A. Klyachin, V. A. Klyachin, “Research in the field of geometric analysis at Volgograd state university”, Mathematical Physics and Computer Simulation, 23:2 (2020), 5–21
Miklyukov V.M., “Some applications of the relative distance of M. A. Lavrent'ev”, Dokl. Math., 71:3 (2005), 404–407
Martio O., Miklyukov V.M., Vuorinen M., “Relative distance and boundary properties of nonparametric surfaces with finite area”, J. Math. Anal. Appl., 286:2 (2003), 524–539
Citation in format AMSBIB
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