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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2016, Volume 22, Number 1, Pages 282–293 (Mi timm1281)  

This article is cited in 5 scientific papers (total in 5 papers)

The construction of singular curves for generalized solutions of eikonal-type equations with a curvature break in the boundary of the boundary set

A. A. Uspenskii, P. D. Lebedev

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
Full-text PDF (569 kB) Citations (5)
References:
Abstract: The problem of singularities appearing in generalized solutions of the boundary value Dirichlet problem for eikonal-type first-order partial differential equations is considered. The object of study is the pseudovertices of the boundary set. Finding the pseudovertices is an element of the procedure for constructing branches of the singular set. Necessary conditions of pseudovertex existence are obtained under weakened assumptions on the smoothness of the boundary of a nonconvex boundary set. The situation of the first-order smoothness of the boundary and breaks of the second-order derivatives is studied. The necessary conditions are written in terms of the stationarity of coordinate functions and with the use of one-sided curvatures.
Keywords: first-order PDE, minimax solution, wavefront, diffeomorphism, eikonal, curvature, optimal result function, singular set, symmetry.
Funding agency Grant number
Russian Science Foundation 15-11-10018
Received: 05.11.2015
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2017, Volume 297, Issue 1, Pages 191–202
DOI: https://doi.org/10.1134/S0081543817050212
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: A. A. Uspenskii, P. D. Lebedev, “The construction of singular curves for generalized solutions of eikonal-type equations with a curvature break in the boundary of the boundary set”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 1, 2016, 282–293; Proc. Steklov Inst. Math. (Suppl.), 297, suppl. 1 (2017), 191–202
Citation in format AMSBIB
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\paper The construction of singular curves for generalized solutions of eikonal-type equations with a curvature break in the boundary of the boundary set
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\vol 22
\issue 1
\pages 282--293
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\jour Proc. Steklov Inst. Math. (Suppl.)
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  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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