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Hölder and Lipschitz Estimates for Viscosity Solutions of Some Degenerate Elliptic PDE’s

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Analysis, Partial Differential Equations and Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 193))

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Abstract

We report here on some recent results, obtained in collaboration with F. Leoni and A. Porretta [7] concerning Hölder and Lipschitz regularity and the solvability of the Dirichlet problem for degenerate quasilinear elliptic equations of the form

$$ - Tr(A(x)D^2 u) + |Du|^p + \lambda u = f(x),x \in \Omega . $$

The research presented here is partly motivated by a paper by J.M. Lasry and P.L. Lions [12]. Our results can be regarded as extensions to the degenerate elliptic case of some of those contained in that paper.

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Authors and Affiliations

  1. Dipartimento di Matematica “Guido Castelnuovo”, Università Roma La Sapienza, Piazzale Aldo Moro, 2, I-00185, Roma

    Italo Capuzzo Dolcetta

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  1. Italo Capuzzo Dolcetta
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Editors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università della Basilicata, Viale dell’Ateneo Lucano 10, 85100, Potenza, Italy

    Alberto Cialdea

  2. Dipartimento di Matematico “Guido Castelnuovo”, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185, Rome, Italy

    Paolo Emilio Ricci  & Flavia Lanzara  & 

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To Prof. V. Maz’ya, with great admiration for his mathematical achievements

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© 2009 Birkhäuser Verlag Basel/Switzerland

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Dolcetta, I.C. (2009). Hölder and Lipschitz Estimates for Viscosity Solutions of Some Degenerate Elliptic PDE’s. In: Cialdea, A., Ricci, P.E., Lanzara, F. (eds) Analysis, Partial Differential Equations and Applications. Operator Theory: Advances and Applications, vol 193. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-9898-9_4

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