Removable Singularities for Quasilinear Elliptic Equations with Source Terms Involving the Solution and Its Gradient

This paper establishes a removable singularity theorem for the quasilinear elliptic equations with source terms like - Δ p u = a | u | q + b | ∇ u | s + c | u | σ | ∇ u | τ with nonnegative bounded Borel measurable functions a , b , c and positive numbers q , s , σ , τ . In particular, we give upper bounds of exponents q , s , σ , τ and a sharp growth condition for nonnegative weak solutions in R N \ E to be extended to the whole of R N as solutions, when E is a compact set satisfying a uniform Minkowski condition.