| The existence problem is solved, and global pointwise estimates of solutions are obtained for quasilinear and Hessian equations of Lane-Emden type, including the following two model problems: -Dpu=uq+m, Fk-u=uq +m,u≥0, on Rn , or on a bounded domain O ⊂ Rn . Here Deltap is the p-Laplacian defined by Deltapu = div (∇u|∇ u|p-2), and Fk[u] is the k-Hessian defined as the sum of k x k principal minors of the Hessian matrix D2u (k = 1, 2,...,n); micro is a nonnegative measurable function (or measure) on O.; The solvability of these classes of equations in the renormalized (entropy) or viscosity sense has been an open problem even for good data micro ∈ Ls(O), s > 1. Such results are deduced from our existence criteria with the sharp exponents nq-p+1pq for the first equation, and s = nq-k2kq for the second one. Furthermore, a complete characterization of removable singularities for each corresponding homogeneous equation is given as a consequence of our solvability results. |
