Concavity maximum principle for viscosity solutions of singular equations. (English) Zbl 1200.35118
Summary: We prove a concavity maximum principle for the viscosity solutions of certain fully nonlinear and singular elliptic and parabolic partial differential equations. Our results parallel and extend those obtained by Korevaar and Kennington for classical solutions of quasilinear equations. Applications are given in the case of the singular infinity Laplace operator.
MSC:
| 35J60 | Nonlinear elliptic equations |
| 35B50 | Maximum principles in context of PDEs |
| 26B25 | Convexity of real functions of several variables, generalizations |
| 35K55 | Nonlinear parabolic equations |
| 35D40 | Viscosity solutions to PDEs |
References:
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