Mappings related to extremal functions for $p$-capacity
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1295-1311.

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

On the Euclidean plane, we consider the class of mappings, whose coordinate functions are extremal functions for $p$-capacity special type condensers.
Mots-clés : Sobolev spaces
Keywords: capacity, extremal functions.
@article{SEMR_2019_16_a141,
     author = {A. S. Romanov},
     title = {Mappings related to extremal functions for $p$-capacity},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1295--1311},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a141/}
}
TY  - JOUR
AU  - A. S. Romanov
TI  - Mappings related to extremal functions for $p$-capacity
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2019
SP  - 1295
EP  - 1311
VL  - 16
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2019_16_a141/
LA  - ru
ID  - SEMR_2019_16_a141
ER  - 
%0 Journal Article
%A A. S. Romanov
%T Mappings related to extremal functions for $p$-capacity
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2019
%P 1295-1311
%V 16
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2019_16_a141/
%G ru
%F SEMR_2019_16_a141
A. S. Romanov. Mappings related to extremal functions for $p$-capacity. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1295-1311. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a141/

[1] A.S. Romanov, “Capacity relations in a flat quadrilateral”, Siberian Math. J., 49:4 (2008), 709–717 | DOI | MR | Zbl

[2] V.M. Gold'shtein, Yu.G. Reshetnyak, Quasiconformal mappings and Sobolev spaces, Kluwer Academic Publishers Group, Dordrecht, 1990 | MR | Zbl

[3] V.G. Maz'ya, Prostranstva S. L. Soboleva, Izd.-vo Leningr. un-ta, Leningrad, 1985 | MR | Zbl

[4] L.C. Evans, R.F. Gariepy, Measure theory and fine properties of functions, CRC Press, Boca Raton, 1992 | MR | Zbl

[5] T. Iwaniec, J.J. Manfredi, “Regularity p-harmonic functions on the plane”, Rev. Mat. Iberoamericana, 5:1–2 (1989), 1–19 | DOI | MR | Zbl

[6] J.J. Manfredi, “p-harmonic functions in the plane”, Proceedings of the AMS, 103:2 (1988), 473–479 | MR | Zbl

[7] B. Bojarski, P. Hajlasz, P. Strzelecki, “Sard's theorem for mappings in Holder and Sobolev spaces”, Manuscripta math., 118:3 (2005), 383–397 | DOI | MR | Zbl

[8] W.P. Ziemer, “Extremal length and conformal capacity”, Trans. Amer. Math. Sos., 126:3 (1967), 460–473 | DOI | MR | Zbl

[9] V.A. Shlyk, “The capacity of a condenser and the modulus of a family of separating surfaces”, Zap. Nauchn. Sem. LOMI, 185, 1990, 168–182 (in Russian) | MR | Zbl

[10] B. Fuglede, “Extremal lenght and functional completion”, Acta math., 98:3–4 (1957), 171–219 | DOI | MR | Zbl

[11] W.P. Ziemer, “Extremal length and $p$-capacity”, Michigan Math. J., 16:1 (1969), 43–51 | DOI | MR | Zbl

[12] A.S. Romanov, “A remark on the properties of nonlinear capacity in $R^3$”, Siberian Math. J., 53:4 (2012), 732–738 | DOI | MR | Zbl