linear elliptic equation

[mona123]

Hi
can someone please help me show that
if A c Rⁿ a domain C² smooth
and f an application is in L2 (A)
and u is a weak solution of the linear elliptic equation.


if f is in C^b (A) with b in (0,1), then u is a classical solution of the linear elliptic equation.
thank you in advance.