The second order estimate for the solution to a singular elliptic boundary value problem
Ling Mi, Bin Liu · Applicable Analysis and Discrete Mathematics · 2012
We study the second order estimate for the unique solution near the boundary to the singular Dirichlet problem -?u = b(x)g(u); u > 0; x ? ?, u|?? = 0, where ? is a bounded domain with smooth boundary in RN, g ? C1((0,?),(0?)), g is decreasing on (0,?) with lim s?0+ g(s) = 1 and g is normalized regularly varying at zero with index ? (? > 1), b ? C?(??) (0 < ? < 1), is positive in ?, may be vanishing on the boundary. Our analysis is based on Karamata regular variation theory.