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Mat. Zametki, 2002, Volume 71, Issue 2, Pages 168–181 (Mi mz337)  

This article is cited in 4 scientific papers (total in 4 papers)

On the Continuity of the Generalized Nemytskii Operator on Spaces of Differentiable Functions

K. O. Besov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We obtain sufficient conditions for the continuity of the general nonlinear superposition operator (generalized Nemytskii operator) acting from the space $C^m(\overline \Omega)$ of differentiable functions on a bounded domain $\Omega$ to the Lebesgue space $L_p(\Omega)$. The values of operators on a function $u\in C^m(\overline \Omega)$ are locally determined by the values of both the function $u$ itself and all of its partial derivatives up to order $m$ inclusive. In certain particular cases, the sufficient conditions obtained are proved to be necessary as well. The results are illustrated by several examples, and an application to the theory of Sobolev spaces is also given.

DOI: https://doi.org/10.4213/mzm337

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English version:
Mathematical Notes, 2002, 71:2, 154–165

Bibliographic databases:

UDC: 517.988.5
Received: 10.08.2001

Citation: K. O. Besov, “On the Continuity of the Generalized Nemytskii Operator on Spaces of Differentiable Functions”, Mat. Zametki, 71:2 (2002), 168–181; Math. Notes, 71:2 (2002), 154–165

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. Besov, KO, “Eigenfunctions of some nonlinear nonlocal operators”, Differential Equations, 38:4 (2002), 510  mathnet  crossref  mathscinet  zmath  isi  scopus  scopus
    2. Walczak, J, “Simplified models of nonlinear multipoles in frequency domain”, Przeglad Elektrotechniczny, 85:4 (2009), 227  mathscinet  isi  elib
    3. Gulgowski J., “Approximation of Solutions to Second Order Nonlinear Picard Problems with Caratheodory Right-Hand Side”, Cent. Eur. J. Math., 12:1 (2014), 155–166  crossref  mathscinet  zmath  isi  scopus  scopus
    4. Beldzinski M., Galewski M., Steglinski R., “Solvability of Abstract Semilinear Equations By a Global Diffeomorphism Theorem”, Results Math., 73:3 (2018), UNSP 122  crossref  mathscinet  isi  scopus
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