{"ID":2867518,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.17402","arxiv_id":"2509.17402","title":"On the vanishing viscosity limit of Hamilton-Jacobi equations with nearly optimal discount","abstract":"In this paper, we establish the convergence of solutions to the viscous Hamilton-Jacobi equation (with a Tonelli Hamiltonian): \\[ λu +H(x, du)=\\varepsilon(λ)Δu,\\quad λ\u003e0 \\] as $λ\\rightarrow 0_+$, once the modulus $\\varepsilon(λ)$ satisfies $\\varlimsup_{λ\\rightarrow 0_+}\\varepsilon(λ)/λ=0$. Such an exponent of $\\varepsilon(λ)$ is nearly optimal in the convergence.","short_abstract":"In this paper, we establish the convergence of solutions to the viscous Hamilton-Jacobi equation (with a Tonelli Hamiltonian): \\[ λu +H(x, du)=\\varepsilon(λ)Δu,\\quad λ\u003e0 \\] as $λ\\rightarrow 0_+$, once the modulus $\\varepsilon(λ)$ satisfies $\\varlimsup_{λ\\rightarrow 0_+}\\varepsilon(λ)/λ=0$. Such an exponent of $\\varepsi...","url_abs":"https://arxiv.org/abs/2509.17402","url_pdf":"https://arxiv.org/pdf/2509.17402v1","authors":"[\"Zibo Wang\",\"Jianlu Zhang\"]","published":"2025-09-22T07:01:10Z","proceeding":"math.AP","tasks":"[\"math.AP\",\"math.DS\",\"math.OC\"]","methods":"[]","has_code":false}