do you know some result for the mixed case of the same form of the previous inequality?

thanks but I need something more specific, the idea is to find elliptic regularity estimation like the one for the following problem −Lapl(u) = f in Omega grad(u) n= g on Lambda so you have ||u||_H^2(Omega) < Cost || f ||_L^2(Omega) + || g ||_H^{1/2}(􀀀Lambda). Do you know some result?