We consider the aymptotic behavior of solutions to the Dirichlet problem for Hamilton-Jacobi equations with large Hamiltonian drift terms. This is an attempt to understand the averaging effect for fully nonlinear elliptic equations. The speaker has already established averaging results for Hamilton-Jacobi equations with convex Hamiltonians under the classical formulation of the Dirichlet condition. In this talk we treat the Dirichlet condition in the viscosity sense and show an averaging result for Hamilton-Jacobi equaions with relatively general Hamiltonians. This is a joint work with Hitoshi Ishii (Tsuda University).

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