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Mat. Sb., 2000, Volume 191, Number 1, Pages 65–102 (Mi msb448)  

This article is cited in 6 scientific papers (total in 6 papers)

Non-linear analytic and coanalytic problems ($L_p$-theory, Clifford analysis, examples)

Yu. A. Dubinskii, A. S. Osipenko

Moscow Power Engineering Institute (Technical University)

Abstract: Two kinds of new mathematical model of variational type are put forward: non-linear analytic and coanalytic problems. The formulation of these non-linear boundary-value problems is based on a decomposition of the complete scale of Sobolev spaces into the “orthogonal” sum of analytic and coanalytic subspaces. A similar decomposition is considered in the framework of Clifford analysis. Explicit examples are presented.

DOI: https://doi.org/10.4213/sm448

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English version:
Sbornik: Mathematics, 2000, 191:1, 61–95

Bibliographic databases:

UDC: 517.53+517.91
MSC: Primary 46E35, 35G30; Secondary 15A66
Received: 28.01.1999

Citation: Yu. A. Dubinskii, A. S. Osipenko, “Non-linear analytic and coanalytic problems ($L_p$-theory, Clifford analysis, examples)”, Mat. Sb., 191:1 (2000), 65–102; Sb. Math., 191:1 (2000), 61–95

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Dubinskii J., Reissig M., “Variational problems in Clifford analysis”, Math. Methods Appl. Sci., 25:14 (2002), 1161–1176  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    2. Dubinskii J.A., “Complex Neumann type boundary problem and decomposition of Lebesgue spaces”, Discrete Contin. Dyn. Syst., 10:1-2 (2004), 201–210  crossref  mathscinet  zmath  isi  elib
    3. Krasnogorsky A.M., “Decomposition of a harmonic space and some applications”, Dokl. Math., 74:3 (2006), 857–859  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    4. I. A. Borovikov, Yu. A. Dubinskii, “Decompositions of the Sobolev–Clifford Modules and Nonlinear Variational Problems”, Proc. Steklov Inst. Math., 260 (2008), 50–67  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    5. Norayr B Engibaryan, “Differential equations where the derivative is taken with respect to a measure”, Sb. Math, 202:2 (2011), 243  mathnet  crossref  mathscinet  isi  scopus
    6. I. A. Borovikov, “Properties of Modules Over Clifford Algebras and Variational Problems”, J Math Sci, 2013  crossref  mathscinet  scopus  scopus  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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