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- W2963552545 abstract "We develop a variational approach to the vanishing discount problem for fully nonlinear, degenerate elliptic, partial differential equations. Under mild assumptions, we introduce viscosity Mather measures for such partial differential equations, which are natural extensions of the Mather measures. Using the viscosity Mather measures, we prove that the whole family of solutions vλ of the discount problem with the factor λ>0 converges to a solution of the ergodic problem as λ→0. On développe une approche variationnelle du problème d'actualisation évanescente pour des équations dégénérées elliptiques complétement non linéaires. Sous des hypothèses relativement faibles, on introduit des mesures de Mather de viscosité pour ces équations aux dérivées partielles, qui sont des extensions naturelles des mesures Mather. En utilisant les mesures de Mather de viscosité, on démontre que toute la famille des solutions vλ du problème d'actualisation de facteur λ>0 converge vers une solution du problème ergodique quand λ→0." @default.
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- W2963552545 date "2017-08-01" @default.
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- W2963552545 title "The vanishing discount problem and viscosity Mather measures. Part 1: The problem on a torus" @default.
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- W2963552545 doi "https://doi.org/10.1016/j.matpur.2016.10.013" @default.
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