Geodesic
On some degenerate elliptic equations arising in geometric problems
Contemporary Mathematics. Fundamental Directions, Proceedings of the Seventh International Conference on Differential and Functional-Differential Equations (Moscow, August 22–29, 2014). Part 1, Tome 58 (2015), pp. 96-110

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We consider some fully nonlinear degenerate elliptic operators and we investigate the validity of certain properties related to the maximum principle. In particular, we establish the equivalence between the sign propagation property and the strict positivity of a suitably defined generalized principal eigenvalue. Furthermore, we show that even in the degenerate case considered in the present paper, the well-known condition introduced by Keller–Osserman on the zero-order term is necessary and sufficient for the existence of entire weak subsolutions. 
@article{CMFD_2015_58_a5,
     author = {I. Capuzzo Dolcetta and F. Leoni and A. Vitolo},
     title = {On some degenerate elliptic equations arising in geometric problems},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {96--110},
     publisher = {mathdoc},
     volume = {58},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2015_58_a5/}
}
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I. Capuzzo Dolcetta; F. Leoni; A. Vitolo. On some degenerate elliptic equations arising in geometric problems. Contemporary Mathematics. Fundamental Directions, Proceedings of the Seventh International Conference on Differential and Functional-Differential Equations (Moscow, August 22–29, 2014). Part 1, Tome 58 (2015), pp. 96-110. http://geodesic.mathdoc.fr/item/CMFD_2015_58_a5/