Boundary estimate of large solution to the k-Hessian equation

This paper investigates boundary blow-up problem of the k-Hessian equation sigma(k)(mu)D(2)u)) = b(z)h(u) in a uniformly (k - 1)-convex domain D subset of R-N, where b(z) grows like delta(-a)(z) as the distance function delta(z) -> 0 and h(u) grows like u(k)(lnu)(beta) as u -> infinity. Boundary estimate of large solution u is obtained by the method of sub- and super-solutions. Compared to previous research (Zhang et al., 2022), this paper provides a more accurate estimate of the large solution when 0 < alpha <1, beta > 2k + 1.