Resumen de Boundary estimates for superharmonic functions and solutions of semilinear elliptic equations with source

Kentaro Hirata

• In a certain Lipschitz domain Ω⊂Rn, we establish the boundary Harnack principle for positive superharmonic functions satisfying the nonlinear differential inequality −Δu?cup, where c?0 and 1?p?(n+α)/(n+α−2) with constant α regarding the lower bound estimate of the Green function on Ω. An argument combined estimates for certain Green potentials and iteration methods enables us to prove it. Results are applicable to positive solutions of semilinear elliptic equations like −Δu=a(x)up with a(x) being nonnegative and bounded on Ω. Also, we present an a priori estimate and a removability theorem for positive solutions having isolated singularities at a boundary point. The former extends one given by Bidaut-Véron and Vivier (Rev Mat Iberoam 16:477–513, 2000) in the case where Ω has a smooth boundary and a(x)≡1.