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.
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Alexander Quaas 1; Boyan Sirakov 2, 3
@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}, }
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/
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