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Zeitschrift für Analysis und ihre Anwendungen


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Volume 19, Issue 4, 2000, pp. 927–951
DOI: 10.4171/ZAA/991

Published online: 2000-12-31

Viscosity Solutions of Nonlinear Systems of Degenerated Elliptic Equations of Second Order

Liu Wei-an[1] and Chen Hua[2]

(1) Wuhan University, Wuhan, Hubei, China
(2) Wuhan University, Wuhan, Hubei, China

In this paper, we discuss the viscosity solutions of Dirichiet problem for weakly coupled systems of fully nonlinear second order degenerated elliptic equations. We prove the existence, uniqueness and continuity of solutions by Perron’s method combined with the technique of coupled solutions. Our results generalize those in [9] for the case of general quasi-monotonic systems.

Keywords: viscosity solutions, systems of partial differential equations, fully nonlinear degenerated elliptic equations, Perron’s method, coupled solution

Wei-an Liu, Hua Chen: Viscosity Solutions of Nonlinear Systems of Degenerated Elliptic Equations of Second Order. Z. Anal. Anwend. 19 (2000), 927-951. doi: 10.4171/ZAA/991