This article is cited in 1 paper

On some degenerate elliptic equations arising in geometric problems

I. Capuzzo Dolcetta^a, F. Leoni^a, A. Vitolo<sup>b

a</sup> Dipartimento di Matematica, Sapienza Università di Roma, Ilaly
^b Dipartimento di Matematica, Università di Salerno, Italy

Abstract: 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.

UDC: 517

 English version: Journal of Mathematical Sciences, 2018, 233:4, 446–461