Need proper justification. I'm using evans pde as reference

Let Q be a bounded and open subset of R". While solving a PDE using Galerkin approximation method, we have shown that the solutions w\" of the approxiamte problems are such that w" are bounded in L20\"), T; H()) and also w\" is bounded in L(0, T; L2). It is concluded that there exists w E L(0, T; 122(9)) n L2H), T; 113(9)) such that for some subsequence of w\