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Graphs with prescribed Levi form trace

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Abstract

We prove existence and uniqueness of a viscosity solution of the Dirichlet problem related to the prescribed Levi mean curvature equation, under suitable assumptions on the boundary data and on the Levi curvature of the domain. We also show that such a solution is Lipschitz continuous by proving that it is the uniform limit of a sequence of classical solutions of elliptic problems and by building Lipschitz continuous barriers.

Keywords: Levi mean curvature, Quasilinear degenerate elliptic PDE’s, Viscosity solutions, Comparison principle, Global Lipschitz estimates

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Authors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Bologna, Piazza di Porta S. Donato 5, 40127, Bologna, Italy

    Vittorio Martino & Annamaria Montanari

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  1. Vittorio Martino
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  2. Annamaria Montanari
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Martino, V., Montanari, A. Graphs with prescribed Levi form trace. Ann. Univ. Ferrara 52, 371–382 (2006). https://doi.org/10.1007/s11565-006-0027-0

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  • DOI: https://doi.org/10.1007/s11565-006-0027-0

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