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Mat. Sb. (N.S.), 1974, Volume 93(135), Number 1, Pages 18–28 (Mi msb2953)  

On the existence of discontinuous solutions for a class of multidimensional quasiregular variational problems

S. F. Morozov


Abstract: In this paper the existence of discontinuous solutions $x^{n+1}=u(x)$, $x\in\Omega$, of a positive definite quasiregular $n$-dimensional variational problem is established when the order of growth of the integrand of the functional degenerates up to unity on non-self-intersecting $(n-1)$-dimensional surfaces lying in the region $\Omega$ or on its boundary $S$.
Bibliography: 11 titles.

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English version:
Mathematics of the USSR-Sbornik, 1974, 22:1, 17–27

Bibliographic databases:

UDC: 519.3
MSC: 49A30
Received: 04.10.1972

Citation: S. F. Morozov, “On the existence of discontinuous solutions for a class of multidimensional quasiregular variational problems”, Mat. Sb. (N.S.), 93(135):1 (1974), 18–28; Math. USSR-Sb., 22:1 (1974), 17–27

Citation in format AMSBIB
\Bibitem{Mor74}
\by S.~F.~Morozov
\paper On the existence of discontinuous solutions for a~class of multidimensional quasiregular variational problems
\jour Mat. Sb. (N.S.)
\yr 1974
\vol 93(135)
\issue 1
\pages 18--28
\mathnet{http://mi.mathnet.ru/msb2953}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=344962}
\zmath{https://zbmath.org/?q=an:0296.49002}
\transl
\jour Math. USSR-Sb.
\yr 1974
\vol 22
\issue 1
\pages 17--27
\crossref{https://doi.org/10.1070/SM1974v022n01ABEH001683}


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