DIRICHLET PROBLEMS FOR SECOND ORDER LINEAR ELLIPTIC EQUATIONS WITH L1-DATA

-div (ADu) + div (ub) + cu = div F in S2 and u = 0 on partial differential S2, where A = [aij] is bounded, uniformly elliptic, and of vanishing mean oscillation (VMO). The main purpose of this paper is to study unique solvability for both problems with L1-data. We prove that if S2 is of class C1, div A + b E Ln,1(S2; Rn), c E Ln2,1(S2) n Ls(S2) for some 1 < s < 32 , and c > 0 in S2, then for each f E L1(S2), there exists a unique weak solution in 1, n n-1 ,infinity W (S2) of the first problem. Moreover, under the additional condition that S2 is of class C1,1 and c E Ln,1(S2), we show that for each FE L1(S2; Rn),