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 -Delta(p)u = a vertical bar u vertical bar(q) + b vertical bar del u vertical bar(s) + c vertical bar u vertical bar(sigma)vertical bar del u vertical bar(tau) with nonnegative bounded Borel measurable functions a, b, c and positive numbers q, s, sigma, tau. In particular, we give upper bounds of exponents q, s, sigma, tau 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.