The space \(W^{k,p}_{\text{loc}}(\Omega)\) (\(p\in [1,\infty)\)) contains all functions which restriction on a compact subset \(U\subset \Omega\) is in the Sobolev space \(W^{k,p}(U)\).
The space \(W^{k,p}_{\text{loc}}(\Omega)\) (\(p\in [1,\infty)\)) contains all functions which restriction on a compact subset \(U\subset \Omega\) is in the Sobolev space \(W^{k,p}(U)\).