On the solutions of quasilinear elliptic problems with boundary blow-up.

*(English)* Zbl 0806.35045
Alvino, Angelo (ed.) et al., Partial differential equations of elliptic type. Proceedings of the conference held October 12-16, 1992 in Cortona, Italy. Cambridge: University Press. Symp. Math. 35, 93-111 (1994).

Summary: Quasilinear elliptic problems are studied which admit solutions tending to infinity on the boundary. The precise asymptotic behaviour is established near the singularities of such solutions. It turns out that the solutions and their gradients are asymptotically independent of the geometry of the boundary. The method developed in this paper uses a coordinate system which flattens the boundary, and is based on a scaling argument.

##### MSC:

35J67 | Boundary values of solutions of elliptic equations |

35J60 | Nonlinear elliptic equations |

35B40 | Asymptotic behavior of solutions of PDE |