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Some Inverse Problems in Periodic Homogenization of Hamilton-Jacobi Equations
Authors:Songting Luo  Hung V Tran  Yifeng Yu
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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