Viscosity solutions of convex Hamilton–Jacobi equations with Neumann conditions satisfy u(x+h,t+σ)+u(x−h,t−σ)−2u(x,t) ≤ C(|h|+σ)^{3/2}, and the 3/2 power is optimal.
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Sharp O(ε log(1/ε)) global and O(ε) almost-everywhere convergence rates are established for periodic homogenization of viscous quadratic Hamilton-Jacobi equations.
Proves 1/2-rate quantitative ergodicity for Hamilton-Jacobi equations in dynamic random media via new almost-Lipschitz regularity for the metric problem.
PDE criteria based on the critical value of the Hamiltonian and viscosity subsolutions determine Lyapunov stability and instability for stationary solutions of contact-type Hamilton-Jacobi equations with continuous convex coercive Hamiltonians.
Under monotonicity, solutions to static contact Hamilton-Jacobi equations with periodicity ε converge uniformly at rate O(ε) to the solution of an effective homogenized equation identified via Mather measures.
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Optimal semiconcavity with fractional modulus for Hamilton-Jacobi equations with Neumann boundary conditions
Viscosity solutions of convex Hamilton–Jacobi equations with Neumann conditions satisfy u(x+h,t+σ)+u(x−h,t−σ)−2u(x,t) ≤ C(|h|+σ)^{3/2}, and the 3/2 power is optimal.
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Sharp global and almost everywhere convergence rates for periodic homogenization of viscous quadratic Hamilton-Jacobi equations
Sharp O(ε log(1/ε)) global and O(ε) almost-everywhere convergence rates are established for periodic homogenization of viscous quadratic Hamilton-Jacobi equations.
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Quantification of ergodicity for Hamilton--Jacobi equations in a dynamic random environment
Proves 1/2-rate quantitative ergodicity for Hamilton-Jacobi equations in dynamic random media via new almost-Lipschitz regularity for the metric problem.
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A PDE formulation of Lyapunov stability for contact-type Hamilton-Jacobi equations
PDE criteria based on the critical value of the Hamiltonian and viscosity subsolutions determine Lyapunov stability and instability for stationary solutions of contact-type Hamilton-Jacobi equations with continuous convex coercive Hamiltonians.
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Quantitative homogenization for static contact Hamilton-Jacobi equations
Under monotonicity, solutions to static contact Hamilton-Jacobi equations with periodicity ε converge uniformly at rate O(ε) to the solution of an effective homogenized equation identified via Mather measures.