# Interpolation of some Sobolev spaces

Let $$X_0=L^2(0,1)$$, $$X_1=H^4(0,1)$$, $$X_2=H^4(0,1)\cap H^2_0(0,1)$$. We know the interpolation space $$(X_0,X_1)_{1/2,2}=H^2(0,1).$$ I am wondering what is $$(X_0,X_2)_{1/2,2}=?$$

Would it be $$H^2_0(0,1)$$?