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Two remarks on Monge-Ampere equations

Lions, Pierre-Louis (1985), Two remarks on Monge-Ampere equations, Annali di Matematica Pura ed Applicata, 142, 1, p. 263-275. http://dx.doi.org/10.1007/BF01766596

Type
Article accepté pour publication ou publié
Date
1985
Journal name
Annali di Matematica Pura ed Applicata
Volume
142
Number
1
Publisher
Springer
Pages
263-275
Publication identifier
Metadata
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Author(s)
Lions, Pierre-Louis
Abstract (EN)
We consider real Monge-Ampère equations and we present two new properties of these equations. First, we show the existence of the «first eigenvalue of Monge-Ampère equation» i.e. we show the existence of a positive constant possessing all the properties of the first eigenvalue of a 2-nd order elliptic operator (positivity, uniqueness of the eigenfunction, maximum principle, bifurcation...).The second property concerns variational characterisations of solutions. Both properties are closely related to similar properties of the general class of Hamilton-Jacobi-Bellman equations.
Subjects / Keywords
Monge-Ampère equations; Hamilton-Jacobi-Bellman equations