A REMARK ON THE SOBOLEV REGULARITY OF CLASSICAL-SOLUTIONS OF STRONGLYELLIPTIC-EQUATIONS

We prove that C-2,C-alpha(<(Omega)over bar>) solutions of problem (1.2 ) below are in Hm+2(Omega) for all m is an element of IN, if f and the coefficients are in H-m(Omega) boolean AND C-0,C-alpha(<(Omega)over b ar>). Previously, this result was explicitly known only if m > n/2 (or if m = 0). A similar result holds for the quasi-linear equation (1.11 ) below.