Geodesic
Partial applicability of Moser's method to nonlinear elliptic systems
Matematičeskie zametki, Tome 58 (1995) no. 4, pp. 547-557.

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

We consider nonlinear elliptic systems of divergent-type second-order partial differential equations with solutions $u\in W_p^1$. It is proved that $Du\in L_q$ with some $q\in(p;+\infty)$ and it is explicitly shown how $q$ depends on the ellipticity modulus of the system. Some conditions on the ellipticity modulus are obtained under which the solutions satisfy the Hölder conditions and the Liouville theorem holds. 
@article{MZM_1995_58_4_a6,
     author = {E. A. Kalita},
     title = {Partial applicability of {Moser's} method to nonlinear elliptic systems},
     journal = {Matemati\v{c}eskie zametki},
     pages = {547--557},
     publisher = {mathdoc},
     volume = {58},
     number = {4},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1995_58_4_a6/}
}
TY  - JOUR
AU  - E. A. Kalita
TI  - Partial applicability of Moser's method to nonlinear elliptic systems
JO  - Matematičeskie zametki
PY  - 1995
SP  - 547
EP  - 557
VL  - 58
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1995_58_4_a6/
LA  - ru
ID  - MZM_1995_58_4_a6
ER  - 
%0 Journal Article
%A E. A. Kalita
%T Partial applicability of Moser's method to nonlinear elliptic systems
%J Matematičeskie zametki
%D 1995
%P 547-557
%V 58
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1995_58_4_a6/
%G ru
%F MZM_1995_58_4_a6
E. A. Kalita. Partial applicability of Moser's method to nonlinear elliptic systems. Matematičeskie zametki, Tome 58 (1995) no. 4, pp. 547-557. http://geodesic.mathdoc.fr/item/MZM_1995_58_4_a6/

[1] Moser Y., “A new proof of de Giorgi's theorem concerning the regularity problem for elliptic differential equations”, Comm. Pure Appl. Math., 13:3 (1960), 457–468 | DOI | MR | Zbl

[2] Koshelev A. I., Regulyarnost reshenii ellipticheskikh uravnenii i sistem, Nauka, M., 1986

[3] Giaquinta M., Necas J., “On the regularity of weak solutions to non linear elliptic systems of partial differential equations”, J. Reine Angew. Math., 316 (1980), 140–159 | MR | Zbl

[4] Kalita E. A., “Regulyarnost reshenii ellipticheskikh sistem vtorogo poryadka”, Izv. vuzov. Matem., 1989, no. 11, 37–46 | MR

[5] Skrypnik I. V,, Metody issledovaniya nelineinykh ellipticheskikh granichnykh zadach, Nauka, M., 1990

[6] Da Prato G., “Spazi ${\frak L}^{(p,\theta )}(\Omega,\delta )$ e loro properieta”, Ann. Math. Pura Appl., 69 (1965), 383–392 | DOI | MR | Zbl