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Right accessibility of semicontinuous initial data for Hamilton-Jacobi equations
We study Hamilton-Jacobi equations with upper semicontinuous initial data
without convexity assumptions on the Hamiltonian. We analyse the
behavior of generalized u.s.c
solutions at the initial time $t=0$,
and find necessary and sufficient conditions on the Hamiltonian such that the
solution attains the initial data along a sequence (right
accessibility).