Abstract
In this paper, a superlinear elliptic equation whose coefficient diverges on the boundary is studied in any bounded domain Ω under the zero Dirichlet boundary condition. Although the equation has a singularity on the boundary, a solution is smooth on the closure of the domain. Indeed, it is proved that the problem has a positive solution and infinitely many solutions without positivity, which belong to C 1 ( Ω ¯ ) or C 2 ( Ω ¯ ) . Moreover, it is proved that a positive solution has a higher order regularity up to C ∞ ( Ω ¯ ) .
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