A selection principle for viscosity solutions of degenerate viscous Hamilton-Jacobi equations is derived via nonlinear adjoint methods, yielding uniform convergence to any desired ergodic solution expressed through generalized Mather measures and the potential.
Convergence of the solutions of the discounted Hamilton–Jacobi equation: convergence of the discounted solutions.Invent
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A new selection problem for degenerate viscous Hamilton-Jacobi equations
A selection principle for viscosity solutions of degenerate viscous Hamilton-Jacobi equations is derived via nonlinear adjoint methods, yielding uniform convergence to any desired ergodic solution expressed through generalized Mather measures and the potential.