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Power Concavity for Solutions of Nonlinear Elliptic Problems in Convex Domains

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Geometric Properties for Parabolic and Elliptic PDE's

Part of the book series: Springer INdAM Series ((SINDAMS,volume 2))

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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Acknowledgements

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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Authors and Affiliations

  1. Dipartimento di Matematica “U. Dini”, Università di Firenze, viale Morgagni 67/A, 50134, Firenze, Italy

    Massimiliano Bianchini & Paolo Salani

Authors
  1. Massimiliano Bianchini
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  2. Paolo Salani
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Corresponding author

Correspondence to Paolo Salani .

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Editors and Affiliations

  1. Dipartimento di Matematica "U. Dini", Università di Firenze, Viale Morgagni 67/A, Firenze, 50124, Italy

    Rolando Magnanini

  2. Graduate School of Information Sciences, Division of Mathematics, Tohoku University, Sendai, 980-8579, Japan

    Shigeru Sakaguchi

  3. , Dipartimento di Matematica ed Applicazio, Università di Napoli Federico II, Via Cintia, Monte S. Angelo, Napoli, 80126, Italy

    Angelo Alvino

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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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