Dirichlet Problems for Fully Nonlinear Equations with “Subquadratic” Hamiltonians

  • Isabeau BirindelliEmail author
  • Françoise Demengel
  • Fabiana Leoni
Part of the Springer INdAM Series book series (SINDAMS, volume 33)


For a class of fully nonlinear equations having second order operators which may be singular or degenerate when the gradient of the solutions vanishes, and having first order terms with power growth, we prove the existence and uniqueness of suitably defined viscosity solutions of Dirichlet problems and we further show that it is a Lipschitz continuous function.


Inhomogenous equations Degenerate and singular fully nonlinear elliptic PDE Dirichlet problem 

2010Mathematical Subject Classification

35J70 35J75 



Part of this work has been done while the first and third authors were visiting the University of Cergy-Pontoise and the second one was visiting Sapienza University of Rome, supported by INDAM-GNAMPA and Laboratoire AGM Research Center in Mathematics of the University of Cergy-Pontoise.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Isabeau Birindelli
    • 1
    Email author
  • Françoise Demengel
    • 2
  • Fabiana Leoni
    • 1
  1. 1.Dipartimento di MatematicaSapienza Università di RomaRomeItaly
  2. 2.Département de MathématiquesUniversité de Cergy-PontoiseCergy-PontoiseFrance

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