Kentaro Hirata

Boundary growth rates for superharmonic functions satisfying a nonlinear inequality in a Lipschitz domain

In a Lipschitz domain $$\Omega \subset \mathbb {R}^N$$ , we investigate the boundary behavior of positive superharmonic functions u satisfying the nonlinear inequality $$-\Delta u(x)\le cd(x,\partial \Omega )^{-\tau }u(x)^p$$ . Based on the fact that, in some ranges of p and $$\tau $$ , the po...