Vanishing discount problem and the additive eigenvalues on changing domains
نویسندگان
چکیده
Let Ω be a bounded open subset of Rn and H(x,p):Ω×Rn→R continuous Hamiltonian that is convex in the second argument. We study asymptotic behavior, as λ→0+, state-constraint Hamilton–Jacobi equation(Sλ){ϕ(λ)uλ(x)+H(x,Duλ(x))⩽0in(1+r(λ))Ω,ϕ(λ)uλ(x)+H(x,Duλ(x))⩾0on(1+r(λ))Ω‾, corresponding additive eigenvalues, or ergodic constant(Eλ){H(x,Dvλ(x))⩽c(λ)in(1+r(λ))Ω,H(x,Dvλ(x))⩾c(λ)on(1+r(λ))Ω‾. Here, ϕ(λ),r(λ):(0,∞)→R are functions such ϕ nonnegative limλ→0+ϕ(λ)=limλ→0+r(λ)=0. obtain both convergence non-convergence results for equations. Moreover, we provide very first result on expansion eigenvalue c(λ) λ→0+. The main tool use duality representation solution with viscosity Mather measures.
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2022
ISSN: ['1090-2732', '0022-0396']
DOI: https://doi.org/10.1016/j.jde.2022.01.055