Geodesic
Asymptotics of the solution of the nonlinear Dirichlet problem having a~strong singularity near a~corner point
Izvestiya. Mathematics , Tome 25 (1985) no. 3, pp. 531-550

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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. 
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     author = {S. A. Nazarov and K. I. Pileckas},
     title = {Asymptotics of the solution of the nonlinear {Dirichlet} problem having a~strong singularity near a~corner point},
     journal = {Izvestiya. Mathematics },
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     number = {3},
     year = {1985},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1985_25_3_a6/}
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S. A. Nazarov; K. I. Pileckas. Asymptotics of the solution of the nonlinear Dirichlet problem having a~strong singularity near a~corner point. Izvestiya. Mathematics , Tome 25 (1985) no. 3, pp. 531-550. http://geodesic.mathdoc.fr/item/IM2_1985_25_3_a6/