Geodesic
Additive and multiplicative anisotropic estimates for integral norms of differentiable functions on irregular domains
Informatics and Automation, Modern problems of mathematics, mechanics, and mathematical physics, Tome 290 (2015), pp. 293-303 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

For irregular domains $G\subset \mathbb R^n$ satisfying the flexible $\sigma $-cone condition, we establish embedding theorems and Gagliardo–Nirenberg type multiplicative inequalities that are anisotropic with respect to the order of derivatives and integrability exponents. 
@article{TRSPY_2015_290_a23,
     author = {A. Yu. Golovko},
     title = {Additive and multiplicative anisotropic estimates for integral norms of differentiable functions on irregular domains},
     journal = {Informatics and Automation},
     pages = {293--303},
     year = {2015},
     volume = {290},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2015_290_a23/}
}
TY  - JOUR
AU  - A. Yu. Golovko
TI  - Additive and multiplicative anisotropic estimates for integral norms of differentiable functions on irregular domains
JO  - Informatics and Automation
PY  - 2015
SP  - 293
EP  - 303
VL  - 290
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2015_290_a23/
LA  - ru
ID  - TRSPY_2015_290_a23
ER  - 
%0 Journal Article
%A A. Yu. Golovko
%T Additive and multiplicative anisotropic estimates for integral norms of differentiable functions on irregular domains
%J Informatics and Automation
%D 2015
%P 293-303
%V 290
%U http://geodesic.mathdoc.fr/item/TRSPY_2015_290_a23/
%G ru
%F TRSPY_2015_290_a23
A. Yu. Golovko. Additive and multiplicative anisotropic estimates for integral norms of differentiable functions on irregular domains. Informatics and Automation, Modern problems of mathematics, mechanics, and mathematical physics, Tome 290 (2015), pp. 293-303. http://geodesic.mathdoc.fr/item/TRSPY_2015_290_a23/

[1] Besov O.V., “Teorema vlozheniya Soboleva dlya oblasti s neregulyarnoi granitsei”, Mat. sb., 192:3 (2001), 3–26 | DOI | MR | Zbl

[2] Besov O.V., “Integralnye otsenki differentsiruemykh funktsii na neregulyarnykh oblastyakh”, Mat. sb., 201:12 (2010), 69–82 | DOI | MR

[3] Besov O.V., Ilin V.P., Nikolskii S.M., Integralnye predstavleniya funktsii i teoremy vlozheniya, Nauka, M., 1996 | MR

[4] Golovko A.Yu., “Multiplikativnye neravenstva tipa Galyardo–Nirenberga dlya oblastei s neregulyarnoi granitsei”, Tr. MFTI, 4:4 (2012), 31–40

[5] Ilin V.P., “Nekotorye neravenstva v funktsionalnykh prostranstvakh i ikh primenenie k issledovaniyu skhodimosti variatsionnykh protsessov”, Tr. MIAN, 53 (1959), 64–127 | Zbl

[6] Labutin D.A., “Neuluchshaemost neravenstv Soboleva dlya klassa neregulyarnykh oblastei”, Tr. MIAN, 232 (2001), 218–222 | MR | Zbl

[7] Mazya V.G., Prostranstva S.L. Soboleva, Izd-vo LGU, L., 1985 | MR

[8] Sobolev S.L., Nekotorye primeneniya funktsionalnogo analiza v matematicheskoi fizike, Nauka, M., 1988 | MR

[9] Stein I.M., Singulyarnye integraly i differentsialnye svoistva funktsii, Mir, M., 1973 | MR

[10] Trushin B.V., “Teoremy vlozheniya Soboleva dlya nekotorogo klassa anizotropnykh neregulyarnykh oblastei”, Tr. MIAN, 260 (2008), 297–319 | MR | Zbl

[11] Gagliardo E., “Ulteriori proprietà di alcune classi di funzioni in più variabili”, Ricerche Mat., 8 (1959), 24–51 | MR | Zbl

[12] Nirenberg L., “On elliptic partial differential equations”, Ann. Sc. Norm. Super. Pisa. Sci. Fis. Mat. Ser. 3, 13 (1959), 115–162 | MR | Zbl