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Lipschitz Continuous Viscosity Solutions for a Class of Fully Nonlinear Equations on Lie Groups

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Abstract

In this paper, we prove existence and uniqueness of Lipschitz continuous viscosity solutions for Dirichlet problems involving a class a fully non-linear operators on Lie groups. In particular, we consider the elementary symmetric functions of the eigenvalues of the Hessian built with left-invariant vector fields.

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Notes

  1. Remark that the cone \(\varGamma^{m}_{k}\) is invariant with respect to permutation of λ j .

  2. We recall that A is k-admissible if σ j (A)≥0 for every j=1,…,k.

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Authors and Affiliations

  1. SISSA, International School for Advanced Studies, via Bonomea, 265, 34136, Trieste, Italy

    Vittorio Martino

  2. Dipartimento di Matematica, Università di Bologna, piazza di Porta S. Donato 5, 40127, Bologna, Italy

    Annamaria Montanari

Authors
  1. Vittorio Martino
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  2. Annamaria Montanari
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Correspondence to Annamaria Montanari.

Additional information

Communicated by Steven G. Krantz.

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Martino, V., Montanari, A. Lipschitz Continuous Viscosity Solutions for a Class of Fully Nonlinear Equations on Lie Groups. J Geom Anal 24, 169–189 (2014). https://doi.org/10.1007/s12220-012-9332-2

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  • DOI: https://doi.org/10.1007/s12220-012-9332-2

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