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Right accessibility of semicontinuous initial data for Hamilton-Jacobi equations

Publication Date
  • 35-Xx Partial Differential 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).

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