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Izv. Akad. Nauk SSSR Ser. Mat., 1984, Volume 48, Issue 6, Pages 1225–1244 (Mi izv1516)  

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.
Bibliography: 12 titles.

Full text: PDF file (1749 kB)
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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
\Bibitem{NazPil84}
\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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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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