Geodesic
Smooth regularity for solutions of the Levi Monge-Ampère equation
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 12 (2001) no. 2, pp. 115-123

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

We present a smooth regularity result for strictly Levi convex solutions to the Levi Monge-Ampère equation. It is a fully nonlinear PDE which is degenerate elliptic. Hence elliptic techniques fail in this situation and we build a new theory in order to treat this new topic. Our technique is inspired to those introduced in [3] and [8] for the study of degenerate elliptic quasilinear PDE’s related to the Levi mean curvature equation. When the right hand side has the meaning of total curvature of a real hypersurface in $\mathbb{C}^{n+1}$, the Levi Monge-Ampère equation arises in the study of envelopes of holomorphy and has important applications in the theory of holomorphic functions of several complex variables. 
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     author = {Lascialfari, Francesca and Montanari, Annamaria},
     title = {Smooth regularity for solutions of the {Levi} {Monge-Amp\`ere} equation},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {115--123},
     publisher = {mathdoc},
     volume = {Ser. 9, 12},
     number = {2},
     year = {2001},
     zbl = {1097.35061},
     mrnumber = {MR1898454},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_2001_9_12_2_a4/}
}
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Lascialfari, Francesca; Montanari, Annamaria. Smooth regularity for solutions of the Levi Monge-Ampère equation. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 12 (2001) no. 2, pp. 115-123. http://geodesic.mathdoc.fr/item/RLIN_2001_9_12_2_a4/