Comptes Rendus
Partial Differential Equations
Solvability of monotone systems of fully nonlinear elliptic PDE's
Comptes Rendus. Mathématique, Volume 346 (2008) no. 11-12, pp. 641-644.

We study quasimonotone weakly coupled systems of uniformly elliptic equations of Isaac type. We prove results on existence of viscosity solutions of such systems and give a necessary and sufficient condition for such a system to satisfy the comparison principle.

On étudie des systèmes quasi-monotones d'équations complètement non-linéaires, uniformément elliptiques, de type Isaac. On obtient des résultats d'existence de solutions du problème de Dirichlet et une condition nécessaire et suffisante pour qu'un tel système satisfasse le principe de comparaison.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.04.008

Alexander Quaas 1; Boyan Sirakov 2, 3

1 Departamento de Matemática, Universidad Santa María, Avenida España 1680, Casilla 110-V, Valparaíso, Chile
2 UFR SEGMI, Université Paris 10, 92001 Nanterre cedex, France
3 CAMS, EHESS, 54 bd Raspail, 75270 Paris cedex 06, France
@article{CRMATH_2008__346_11-12_641_0,
     author = {Alexander Quaas and Boyan Sirakov},
     title = {Solvability of monotone systems of fully nonlinear elliptic {PDE's}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {641--644},
     publisher = {Elsevier},
     volume = {346},
     number = {11-12},
     year = {2008},
     doi = {10.1016/j.crma.2008.04.008},
     language = {en},
}
TY  - JOUR
AU  - Alexander Quaas
AU  - Boyan Sirakov
TI  - Solvability of monotone systems of fully nonlinear elliptic PDE's
JO  - Comptes Rendus. Mathématique
PY  - 2008
SP  - 641
EP  - 644
VL  - 346
IS  - 11-12
PB  - Elsevier
DO  - 10.1016/j.crma.2008.04.008
LA  - en
ID  - CRMATH_2008__346_11-12_641_0
ER  - 
%0 Journal Article
%A Alexander Quaas
%A Boyan Sirakov
%T Solvability of monotone systems of fully nonlinear elliptic PDE's
%J Comptes Rendus. Mathématique
%D 2008
%P 641-644
%V 346
%N 11-12
%I Elsevier
%R 10.1016/j.crma.2008.04.008
%G en
%F CRMATH_2008__346_11-12_641_0
Alexander Quaas; Boyan Sirakov. Solvability of monotone systems of fully nonlinear elliptic PDE's. Comptes Rendus. Mathématique, Volume 346 (2008) no. 11-12, pp. 641-644. doi : 10.1016/j.crma.2008.04.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.04.008/

[1] J. Busca; B. Sirakov Harnack type estimates for nonlinear elliptic systems and applications, Ann. Inst. H. Poincaré Anal. Nonlinéaire, Volume 21 (2004) no. 5, pp. 543-590

[2] L.A. Caffarelli; M.G. Crandall; M. Kocan; A. Świech On viscosity solutions of fully nonlinear equations with measurable ingredients, Comm. Pure Appl. Math., Volume 49 (1996), pp. 365-397

[3] H. Ishii; S. Koike Viscosity solutions for monotone systems of second-order elliptic PDE's, Comm. Partial Differential Equations, Volume 16 (1991) no. 6–7, pp. 1095-1128

[4] A. Quaas; B. Sirakov Principal eigenvalues and the Dirichlet problem for fully nonlinear operators, C. R. Acad. Sci. Paris, Ser. I, Volume 342 (2006) no. 2, pp. 115-118

[5] A. Quaas; B. Sirakov Principal eigenvalues and the Dirichlet problem for fully nonlinear operators, Adv. Math., Volume 218 (2008) no. 1, pp. 105-135

Cited by Sources:

Comments - Policy