The Inverse Problem for Hamilton--Jacobi Equations and Semiconcave Envelopes
The Inverse Problem for Hamilton--Jacobi Equations and Semiconcave Envelopes
We study the inverse problem, or inverse design problem, for a time-evolution Hamilton--Jacobi equation. More precisely, given a target function $u_T$ and a time horizon $T>0$, we aim to construct all the initial conditions for which the viscosity solution coincides with $u_T$ at time $T$. As is common in this …