Geodesic
Schauder Estimates and Complete Regularity of the Solutions of an Elliptic System
Matematičeskie zametki, Tome 85 (2009) no. 1, pp. 89-97.

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

We study the complete regularity of the solutions of a nondiagonal elliptic system of nonlinear differential equations of divergent form whose coefficients are sufficiently slowly varying functions of their arguments and whose off-diagonal terms are sufficiently small. To this end, we apply a technique based on successive approximations to the solution and the use of Schauder estimates at each step.
Keywords: nonlinear differential equation, elliptic system, Schauder estimate, complete regularity of solutions, Dirichlet boundary condition, Hölder continuity. 
@article{MZM_2009_85_1_a7,
     author = {D. V. Portnyagin},
     title = {Schauder {Estimates} and {Complete} {Regularity} of the {Solutions} of an {Elliptic} {System}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {89--97},
     publisher = {mathdoc},
     volume = {85},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_85_1_a7/}
}
TY  - JOUR
AU  - D. V. Portnyagin
TI  - Schauder Estimates and Complete Regularity of the Solutions of an Elliptic System
JO  - Matematičeskie zametki
PY  - 2009
SP  - 89
EP  - 97
VL  - 85
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2009_85_1_a7/
LA  - ru
ID  - MZM_2009_85_1_a7
ER  - 
%0 Journal Article
%A D. V. Portnyagin
%T Schauder Estimates and Complete Regularity of the Solutions of an Elliptic System
%J Matematičeskie zametki
%D 2009
%P 89-97
%V 85
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2009_85_1_a7/
%G ru
%F MZM_2009_85_1_a7
D. V. Portnyagin. Schauder Estimates and Complete Regularity of the Solutions of an Elliptic System. Matematičeskie zametki, Tome 85 (2009) no. 1, pp. 89-97. http://geodesic.mathdoc.fr/item/MZM_2009_85_1_a7/

[1] E. De Giorgi, “Un esempio di estremali discontinue per un problema variazionale di tipo ellittico”, Boll. Un. Mat. Ital. (4), 1 (1968), 135–137 | MR | Zbl

[2] C. B. Morrey, jr., “Partial regularity results for non-linear elliptic systems”, J. Math. Mech., 17 (1968), 649–670 | MR | Zbl

[3] E. Guisti, M. Miranda, “Sulla regolaritá delle soluzioni deboli di una classe di sistemi ellittici quasi-lineari”, Arch. Rational Mech. Anal., 31 (1968), 173–184 | MR | Zbl

[4] L. Pepe, “Risultati di regolaritá parziale per le soluzioni $\mathscr H^{1,p}(\Omega)$, $1

2$, di sistemi ellittici quasi-lineari”, Ann. Univ. Ferrara Sez. VII (N.S.), 16 (1971), 129–148 | MR | Zbl

[5] Y.-Z. Chen, L.-C. Wu, Second Order Elliptic Equations and Elliptic Systems, Transl. Math. Monogr., 174, Amer. Math. Soc., Providence, RI, 1998 | MR | Zbl