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Article Dans Une Revue Dynamics of Continuous, Discrete and Impulsive Systems - Series A : Mathematical Analysis Année : 2021

Ergodic pairs for degenerate pseudo Pucci's fully nonlinear operators

ergodique paires pour des opérateurs de type Pseu Pucci

Françoise Demengel
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Résumé

We study the ergodic problem for fully nonlinear operators which may be singular or degenerate when at least one of the compoenents of the gradient of solutions vanishes. We prove the convergence of both explosive solutions and solutions of Dirichlet problems for approximating equations. We further characterize the ergodic constant as the infimum of constants for which there exist bounded sub solutions. As intermediate results of independent interest, we prove a priori Lipschitz estimates depending only on the norm of the zeroth order term, and a comparison principle for equations having no zero order terms.
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Dates et versions

hal-04445309 , version 1 (07-02-2024)

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  • HAL Id : hal-04445309 , version 1

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Françoise Demengel. Ergodic pairs for degenerate pseudo Pucci's fully nonlinear operators: The problem ergodic for Pseudo Pucci's operators. Dynamics of Continuous, Discrete and Impulsive Systems - Series A : Mathematical Analysis , 2021, 41 (7), pp.3021-3029. ⟨hal-04445309⟩
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