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Asymptotics of the solution of the nonlinear Dirichlet problem having a strong singularity near a corner point
S. A. Nazarov, K. I. Pileckas
Abstract:
The asymptotics of the solutions of the Dirichlet problem for the equation
$$
-\Delta u(x)+u(x)^{2k+1}=f(x),\qquad x\in\Omega,
$$
is studied in a plane domain $\Omega$ with a corner point of angle $\alpha$. The asymptotics of a solution of this problem is constructed in the case where the right side $f$ has a strong singularity near the corner point.
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English version:
Mathematics of the USSR-Izvestiya, 1985, 25:3, 531–550
Bibliographic databases:
UDC:
517.9
MSC: 35J65, 35B40 Received: 31.01.1983
Citation:
S. A. Nazarov, K. I. Pileckas, “Asymptotics of the solution of the nonlinear Dirichlet problem having a strong singularity near a corner point”, Izv. Akad. Nauk SSSR Ser. Mat., 48:6 (1984), 1225–1244; Math. USSR-Izv., 25:3 (1985), 531–550
Citation in format AMSBIB
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\by S.~A.~Nazarov, K.~I.~Pileckas
\paper Asymptotics of the solution of the nonlinear Dirichlet problem having a~strong singularity near a~corner point
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1984
\vol 48
\issue 6
\pages 1225--1244
\mathnet{http://mi.mathnet.ru/izv1516}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=772114}
\zmath{https://zbmath.org/?q=an:0599.35068|0577.35039}
\transl
\jour Math. USSR-Izv.
\yr 1985
\vol 25
\issue 3
\pages 531--550
\crossref{https://doi.org/10.1070/IM1985v025n03ABEH001305}
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http://mi.mathnet.ru/eng/izv1516 http://mi.mathnet.ru/eng/izv/v48/i6/p1225
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