BOUNDARY BEHAVIOR OF SOLUTIONS TO A SINGULAR DIRICHLET PROBLEM WITH A NONLINEAR CONVECTION

In this article we analyze the exact boundary behavior of solutions to the singular nonlinear Dirichlet problem -Delta u = b(x)g(u) + lambda vertical bar del u vertical bar(q) + sigma, u > 0, x is an element of Omega, u vertical bar(partial derivative Omega) = 0, where Omega is a bounded domain with smooth boundary in R-N, q is an element of (0, 2], sigma > 0, lambda > 0, g is an element of C-1((0,infinity), (0, infinity)), lim(delta -> 0)+g(s) = infinity, g is decreasing on (0, s(0)) for some s(0) > 0, b is an element of C-loc(alpha)(Omega) for some alpha is an element of (0, 1), is positive in Omega, but may be vanishing or singular on the boundary. We show that lambda vertical bar del u vertical bar(q) does not affect the first expansion of classical solutions near the boundary.