A local inverse problem for Hamilton-Jacobi equation Reconstruction of Riemannian metric

I.V. Golubyatnikov, Hilmi H. Hacisalihou?lu


We study the uniqueness questions for the inverse problem of determining hamiltonian H(x,p)= gij (x) pi pj and a phase function w(x,t) from the Hamilton-Jacobi equation and the initial-terminal conditions w(x, t0 ), w(x, t1). Here the unknown functions gij(x) compose a matrix inverse to that of the metric tensor. We obtain uniqueness theorems for special classes of initial-terminal conditions in the cases n =1, n=2 and in the case of a scalar n/span>n matrix gij(x).


Inverse problem, hamiltonian, Hamilton system, trajectories

Full Text: