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- W4310080593 abstract "Suppose M is a closed Riemannian manifold. For a $$C^2$$ generic (in the sense of Mañé) Tonelli Hamiltonian $$H: T^*Mrightarrow mathbb {R}$$ , the minimal viscosity solution $$u_lambda ^-:Mrightarrow mathbb {R}$$ of the negative discounted equation $$begin{aligned} -lambda u+H(x,d_xu)=c(H),quad xin M, lambda >0 end{aligned}$$ with the Mañé’s critical value c(H) converges to a uniquely established viscosity solution $$u_0^-$$ of the critical Hamilton–Jacobi equation $$begin{aligned} H(x,d_x u)=c(H),quad xin M end{aligned}$$ as $$lambda rightarrow 0_+$$ . We also propose a dynamical interpretation of $$u_0^-$$ ." @default.
- W4310080593 created "2022-11-30" @default.
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- W4310080593 date "2022-11-24" @default.
- W4310080593 modified "2023-09-27" @default.
- W4310080593 title "On the Negative Limit of Viscosity Solutions for Discounted Hamilton–Jacobi Equations" @default.
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- W4310080593 doi "https://doi.org/10.1007/s10884-022-10227-1" @default.
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