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Mat. Zametki, 2011, Volume 90, Issue 6, Pages 918–946 (Mi mz8556)  

This article is cited in 2 scientific papers (total in 2 papers)

Stability of Unique Solvability of Quasilinear Equations Given Additional Data

I. G. Tsar'kov

M. V. Lomonosov Moscow State University

Abstract: We study quasilinear equations of elliptic and parabolic type whose solutions, having bounded uniform norms or bounded uniform norms of their derivatives, are uniquely defined by the additional information about the values of these solutions on a grid. For the case in which the equations and grid values are given with an error, we present estimates of the error of approximate solutions in the uniform metric.

Keywords: quasilinear equation of elliptic or parabolic type, stability of unique solvability, quasilinear equation, Dirichlet boundary-value problem, Banach space, Lipschitz function, $\varepsilon$-grid, star-shaped set, Friedrichs inequality

DOI: https://doi.org/10.4213/mzm8556

Full text: PDF file (593 kB)
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English version:
Mathematical Notes, 2011, 90:6, 894–919

Bibliographic databases:

UDC: 517.9
Received: 16.05.2009
Revised: 15.03.2011

Citation: I. G. Tsar'kov, “Stability of Unique Solvability of Quasilinear Equations Given Additional Data”, Mat. Zametki, 90:6 (2011), 918–946; Math. Notes, 90:6 (2011), 894–919

Citation in format AMSBIB
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\by I.~G.~Tsar'kov
\paper Stability of Unique Solvability of Quasilinear Equations Given Additional Data
\jour Mat. Zametki
\yr 2011
\vol 90
\issue 6
\pages 918--946
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\crossref{https://doi.org/10.4213/mzm8556}
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\transl
\jour Math. Notes
\yr 2011
\vol 90
\issue 6
\pages 894--919
\crossref{https://doi.org/10.1134/S0001434611110289}
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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. A. R. Alimov, I. G. Tsar'kov, “Connectedness and other geometric properties of suns and Chebyshev sets”, J. Math. Sci., 217:6 (2016), 683–730  mathnet  crossref  mathscinet
    2. A. R. Alimov, I. G. Tsar'kov, “Connectedness and solarity in problems of best and near-best approximation”, Russian Math. Surveys, 71:1 (2016), 1–77  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Математические заметки Mathematical Notes
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