Geodesic
A second look on definition and equivalent norms of Sobolev spaces
Mathematica Bohemica, Tome 124 (1999) no. 2-3, pp. 315-328.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Sobolev's original definition of his spaces $L^{m,p}(\Omega)$ is revisited. It only assumed that $\Omega\subseteq\Bbb R^n$ is a domain. With elementary methods, essentially based on Poincare'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.
DOI : 10.21136/MB.1999.126243
Classification : 46E35
Keywords: Sobolev spaces; Poincaré’s inequality; existence of intermediate derivates 
@article{10_21136_MB_1999_126243,
     author = {Naumann, J. and Simader, C. G.},
     title = {A second look on definition and equivalent norms of {Sobolev} spaces},
     journal = {Mathematica Bohemica},
     pages = {315--328},
     publisher = {mathdoc},
     volume = {124},
     number = {2-3},
     year = {1999},
     doi = {10.21136/MB.1999.126243},
     mrnumber = {1780700},
     zbl = {0941.46019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.1999.126243/}
}
TY  - JOUR
AU  - Naumann, J.
AU  - Simader, C. G.
TI  - A second look on definition and equivalent norms of Sobolev spaces
JO  - Mathematica Bohemica
PY  - 1999
SP  - 315
EP  - 328
VL  - 124
IS  - 2-3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.1999.126243/
DO  - 10.21136/MB.1999.126243
LA  - en
ID  - 10_21136_MB_1999_126243
ER  - 
%0 Journal Article
%A Naumann, J.
%A Simader, C. G.
%T A second look on definition and equivalent norms of Sobolev spaces
%J Mathematica Bohemica
%D 1999
%P 315-328
%V 124
%N 2-3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.1999.126243/
%R 10.21136/MB.1999.126243
%G en
%F 10_21136_MB_1999_126243
Naumann, J.; Simader, C. G. A second look on definition and equivalent norms of Sobolev spaces. Mathematica Bohemica, Tome 124 (1999) no. 2-3, pp. 315-328. doi : 10.21136/MB.1999.126243. http://geodesic.mathdoc.fr/articles/10.21136/MB.1999.126243/

Cité par Sources :