Problem 4. Let U in R" be a bounded domain. L a uniformly elliptic second order linear differential operator on U, with coefficients that are in C*(U). a) Show that every solution u of Lu = 0 is in C*(U). b) Show: every sequence {uk} =1 of solutions of Lu = 0) that is bounded in L(U) contains a subsequence which converges uniformly on compact subsets of U. Problem 4. Let U in R" be a bounded domain. L a uniformly elliptic second order linear differential operator on U, with coefficients that are in C*(U). a) Show that every solution u of Lu = 0 is in C*(U). b) Show: every sequence {uk} =1 of solutions of Lu = 0) that is bounded in L(U) contains a subsequence which converges uniformly on compact subsets of U