Abstract
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.
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Acknowledgements
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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Birindelli, I., Demengel, F., Leoni, F. (2019). Dirichlet Problems for Fully Nonlinear Equations with “Subquadratic” Hamiltonians. In: Dipierro, S. (eds) Contemporary Research in Elliptic PDEs and Related Topics. Springer INdAM Series, vol 33. Springer, Cham. https://doi.org/10.1007/978-3-030-18921-1_2
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DOI: https://doi.org/10.1007/978-3-030-18921-1_2
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