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Sibirskii Matematicheskii Zhurnal, 2007, Volume 48, Number 4, Pages 789–810 (Mi smj1745)  
This article is cited in 5 scientific papers (total in 5 papers)

Necessary and sufficient conditions for a curve to be the gradient range of a $C^1$-smooth function

M. V. Korobkova, E. Yu. Panovb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Novgorod State University after Yaroslav the Wise
Full-text PDF (497 kB) Citations (5)
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Abstract: We find some necessary and sufficient conditions for a plane curve to be the gradient range of a $C^1$-smooth function of two variables. As one of the consequences we give the necessary and sufficient conditions on a continuous function $\varphi$ under which the differential equation $\dfrac{\partial v}{\partial t}=\varphi\biggl(\dfrac{\partial v}{\partial x}\biggr)$ has nontrivial $C^1$-smooth solutions.
Keywords: $C^1$-smooth function, gradient range, curve.
Received: 25.01.2006
English version:
Siberian Mathematical Journal, 2007, Volume 48, Issue 4, Pages 629–647
DOI: https://doi.org/10.1007/s11202-007-0065-6
Bibliographic databases:
Language: Russian
Citation: M. V. Korobkov, E. Yu. Panov, “Necessary and sufficient conditions for a curve to be the gradient range of a $C^1$-smooth function”, Sibirsk. Mat. Zh., 48:4 (2007), 789–810; Siberian Math. J., 48:4 (2007), 629–647
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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