期刊
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
卷 245, 期 2, 页码 809-817出版社
SPRINGER
DOI: 10.1007/s00205-022-01797-x
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We studied a problem concerning the Hamilton-Jacobian equation, where the Hamiltonian is periodic, coercive, and convex. By combining the representation formula from optimal control theory and a theorem by Alexander, we obtained a homogenized rate that is close to optimal and holds in all dimensions.
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.
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