Abstract
We investigate convexity properties of solutions to elliptic Dirichlet problems in convex domains. In particular we give conditions on the operator F such that a suitable power of a positive solution u of a fully nonlinear equation F(x,u,Du,D 2 u)=0 in a convex domain Ω, vanishing on ∂Ω, is concave.
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We thank two unknown referees for their careful reading and for several useful suggestions that helped us to improve the paper.
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Bianchini, M., Salani, P. (2013). Power Concavity for Solutions of Nonlinear Elliptic Problems in Convex Domains. In: Magnanini, R., Sakaguchi, S., Alvino, A. (eds) Geometric Properties for Parabolic and Elliptic PDE's. Springer INdAM Series, vol 2. Springer, Milano. https://doi.org/10.1007/978-88-470-2841-8_3
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DOI: https://doi.org/10.1007/978-88-470-2841-8_3
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