In the book Sobolev Spaces with Application of Maz’ya, $ \mathring {L^k_p}(\Omega)$ is defined to be the completion of $ \mathcal D(\Bbb R^n)$ under the norm $ ||\nabla^ku||_{L_p(\Omega)}$ . For nice domain (and correct values of $ k,p,q,n$ ), Sobolev’s embedding theory tell us that $ \mathring {L^k_p}(\Omega)\hookrightarrow L_q(\Omega)$ continuously. However, I am having aRead more