Geodesic
Sharpness of Sobolev Inequalities for a~Class of Irregular Domains
Informatics and Automation, Function spaces, harmonic analysis, and differential equations, Tome 232 (2001), pp. 218-222

Voir la notice de l'article provenant de la source Math-Net.Ru

Recently, O. V. Besov proved the embedding $W^{m}_p(\Omega)\subset L_q(\Omega)$ for the Sobolev spaces of higher orders $m=2,3,\ldots $ over a domain $\Omega\subset\mathbb R^n$ satisfying $s$-John condition. We show that the number $q$ obtained by Besov in this embedding is maximal over the class of $s$-John domains. An unimprovable embedding of the Sobolev spaces $W^1_p(\Omega )$ was found earlier in works of Hajłasz and Koskela and of Kilpeläinen and Malý. 
@article{TRSPY_2001_232_a17,
     author = {D. A. Labutin},
     title = {Sharpness of {Sobolev} {Inequalities} for {a~Class} of {Irregular} {Domains}},
     journal = {Informatics and Automation},
     pages = {218--222},
     publisher = {mathdoc},
     volume = {232},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2001_232_a17/}
}
TY  - JOUR
AU  - D. A. Labutin
TI  - Sharpness of Sobolev Inequalities for a~Class of Irregular Domains
JO  - Informatics and Automation
PY  - 2001
SP  - 218
EP  - 222
VL  - 232
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2001_232_a17/
LA  - ru
ID  - TRSPY_2001_232_a17
ER  - 
%0 Journal Article
%A D. A. Labutin
%T Sharpness of Sobolev Inequalities for a~Class of Irregular Domains
%J Informatics and Automation
%D 2001
%P 218-222
%V 232
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2001_232_a17/
%G ru
%F TRSPY_2001_232_a17
D. A. Labutin. Sharpness of Sobolev Inequalities for a~Class of Irregular Domains. Informatics and Automation, Function spaces, harmonic analysis, and differential equations, Tome 232 (2001), pp. 218-222. http://geodesic.mathdoc.fr/item/TRSPY_2001_232_a17/