Boundary singularity problem of some nonlinear elliptic equations (Q5933613)

The author studies the limit properties of solutions to the boundary singularity problem \(Lu=u^{\alpha}\) in \(D\), with \(u|_{\partial D\setminus\{0\}}\), \(1<\alpha\leq 2\), where \(L\) is a uniformly elliptic operator in \(\mathbb R^{d}\), \(D\) is a \(C^{2}\)-domain in \(\mathbb R^{d}\) with boundary \(\partial D\). The paper contains a result concerning the limit behaviour of classical non-negative solutions near the singular point 0. In the proof one uses Green functions associated to the operator \(L\) and to the \((L,\alpha)\)-superdiffusion.