• Corpus ID: 239016278

A near-optimal rate of periodic homogenization for convex Hamilton-Jacobi equations

@inproceedings{Cooperman2021ANR,
  title={A near-optimal rate of periodic homogenization for convex Hamilton-Jacobi equations},
  author={William Cooperman},
  year={2021}
}
We consider a Hamilton-Jacobi equation where the Hamiltonian is periodic in space and coercive and convex in momentum. Combining the representation formula from optimal control theory and a theorem of Alexander, originally proved in the context of first-passage percolation, we find a rate of homogenization which is within a log-factor of optimal and holds in all dimensions. 

References

SHOWING 1-10 OF 11 REFERENCES
On the rate of convergence in homogenization of Hamilton-Jacobi equations
We consider the homogenization problem for fully nonlinear first order scalar partial differential equations of Hamilton-Jacobi type such as u(x) + H ( x, x ! , Du(x) ) = 0, x ∈ R , where ! is a
Approximation of subadditive functions and convergence rates in limiting-shape results
For a nonnegative subadditive function h on Z d , with limiting approximation g(x) = lim n h(nx)/n, it is of interest to obtain bounds on the discrepancy between g(x) and h(x), typically of order |x|
Rate of Convergence in Periodic Homogenization of Hamilton–Jacobi Equations: The Convex Setting
AbstractWe study the rate of convergence of $${u^\varepsilon}$$uε, as $${\varepsilon \to 0+}$$ε→0+, to u in periodic homogenization of Hamilton–Jacobi equations. Here, $${u^\varepsilon}$$uε and u are
Hamilton-Jacobi equations : theory and applications
  • Providence, Rhode Island: American Mathematical Society,
  • 2021
Burago. “Periodic metrics
  • Advances in Soviet Mathematics
  • 1992
Periodic metrics
  • Advances in Soviet Mathematics
  • 1992
Homogenization of Hamilton-Jacobi equations
  • 1987
A Moment Problem in L1 Approximation
  • Proceedings of the American Mathematical Society
  • 1965
Hobby and John R . Rice . “ A Moment Problem in L 1 Approximation ”
...
1
2
...