Abstract
We look at the effective Hamiltonian \({\overline{H}}\) associated with the Hamiltonian \({H(p,x)=H(p)+V(x)}\) in the periodic homogenization theory. Our central goal is to understand the relation between \({V}\) and \({\overline{H}}\). We formulate some inverse problems concerning this relation. Such types of inverse problems are, in general, very challenging. In this paper, we discuss several special cases in both convex and nonconvex settings.
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Communicated by W. E
The work of SL is partially supported by NSF Grant DMS-1418908, the work of HT is partially supported by NSF Grants DMS-1361236 and DMS-1615944, and the work of YY is partially supported by NSF CAREER award #1151919.
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Luo, S., Tran, H.V. & Yu, Y. Some Inverse Problems in Periodic Homogenization of Hamilton-Jacobi Equations. Arch Rational Mech Anal 221, 1585–1617 (2016). https://doi.org/10.1007/s00205-016-0993-z
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DOI: https://doi.org/10.1007/s00205-016-0993-z