an:01406919
Zbl 0941.46019
Naumann, J.; Simader, C. G.
A second look on definition and equivalent norms of Sobolev spaces
EN
Math. Bohem. 124, No. 2-3, 315-328 (1999).
00063694
1999
j
46E35
Sobolev spaces; Poincar??'s inequality; existence of intermediate derivates
Summary: Sobolev's original definition of his spaces \(L^{m,p}(\Omega)\) is revisited. It is only assumed that \(\Omega \subseteq \mathbb R^n\) is a domain. With elementary methods, essentially based on Poincar??'s inequality for balls (or cubes), the existence of intermediate derivates of functions \(u\in L^{m,p}(\Omega)\) with respect to appropriate norms, and equivalence of these norms is proved.