Open AccessThe second order estimate for the solution to a singular elliptic boundary value problem
Author(s) -
Ling Mi,
Bin Liu
Publication year - 2012
Publication title -
applicable analysis and discrete mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.69
H-Index - 26
eISSN - 2406-100X
pISSN - 1452-8630
DOI - 10.2298/aadm120713018m
Subject(s) - mathematics , bounded function , boundary (topology) , domain (mathematical analysis) , order (exchange) , boundary value problem , dirichlet distribution , mathematical analysis , boundary values , dirichlet problem , dirichlet boundary condition , zero (linguistics) , singular value , pure mathematics , eigenvalues and eigenvectors , linguistics , philosophy , physics , finance , quantum mechanics , economics
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.