TY - JOUR
T1 - On the rate of convergence in homogenization of Hamilton-Jacobi equations
AU - Capuzzo-Dolcetta, I.
AU - Ishii, H.
PY - 2001/9
Y1 - 2001/9
N2 - 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.
AB - 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.
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M3 - Article
AN - SCOPUS:0039300006
VL - 50
SP - 1113
EP - 1128
JO - Indiana University Mathematics Journal
JF - Indiana University Mathematics Journal
SN - 0022-2518
IS - 3
ER -