Summability of solutions of second-order nonlinear elliptic equations with data in classes close to L1

In this paper, we consider the Dirichlet problem in a bounded open set Omega subset of R-n (n >= 2) for a class of second-order nonlinear elliptic equations with right-hand side f in L-1(Omega). We study the summability of entropy and weak solutions of this problem under the stronger assumption that f G(vertical bar f vertical bar)is an element of L-1(Omega), where G is a nonnegative increasing continuous function on [0,+ infinity). We show how the summability of the solutions depends on the function G. Our conditions on G imply that L1+epsilon(Omega) subset of K-G subset of L-1( Omega) for every epsilon > 0, where KG is the set of all measurable functions v on Omega such that v(G)(vertical bar v vertical bar) is an element of L-1(Omega).