Notes on removable singularities for a certain class of semilinear degenerate elliptic equations

Abstract

When α=β=γ=0, this result is already established by H. Brezis and L. Veron in [BV]. They proved this result by using a comparison principle and a weak maximum principle. Although the operator in this paper is degenerate at the origin, their methods still work under some modifications. In fact we first construct a suitable super-solution, and then we derive a pointwise estimate by a weak muximum principle and Kato's inequality. As a application we will deduce that if u∈(C2(B') satisfies