Boundary Behavior of Solutions to Singular Boundary Value Problems for Nonlinear Elliptic Equations

摘要

Let 11 be a bounded domain with smooth boundary in R N and h E C0, cc), (0, co)) with lims _,0+ h(s) = T E (0, co). By the perturbation method,which is due to Garcia Melian, and nonlinear transformations and comparison principles, we derive the exact boundary behavior of solutions to a singular Dirichlet problem -Av + IVvi2 = b(x), v > 0, x E 12, vian = 0. Then, applying the result, combining two kinds of nonlinear transformations, we derive the exact boundary behavior of solutions to a boundary blow-up elliptic problem and a singular Dirichlet problem, where the weight b is positive in Q and may be (rapidly) vanishing or blow up on the boundary.