We consider the homogenization problem for fully nonlinear first order scalar partial differential equations of Hamilton-Jacobi type such as uε(x) + H (x, x/ε, Duε(x)) = 0, x ∈ ℝN, where ε is a small positive parameter and H is a periodic function of the second variable. Our main results (Theorems 1.1 and 1.2 below) give estimates on the rate of convergence of uε to the solution U of the homogenized problem u(x) + H̄(x, Du(x)) = 0, x ∈ ℝN.
|Number of pages||16|
|Journal||Indiana University Mathematics Journal|
|Publication status||Published - 2001 Sep|
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