Minimal Lp-solutions to singular sublinear elliptic problems

We solve the existence problem for the minimal positive solutions u is an element of L- p (ohm, dx) to the Dirichlet problems for sublinear elliptic equations of the form { Lu = sigma u(q) + mu in ohm, lim inf (x -> y) u(x) = 0 y is an element of partial derivative(infinity)ohm,where 0 < q < 1 and Lu := -div(A(x)del u) is a linear uniformly elliptic operator with bounded measurable coefficients. The coefficient sigma and data mu are nonnegative Radon measures on an arbitrary domain ohm subset of R- n with a positive Green function associated with L. Our techniques are based on the use of sharp Green potential pointwise estimates, weighted norm inqualities, and norm estimates in terms of generalized energy.