We consider periodic homogenization of the fully nonlinear uniformly elliptic equation u(epsilon) + H(x, x/epsilon, Du(epsilon), D(2)u(epsilon)) = 0. We give an estimate of the rate of convergence of ue to the solution u of the homogenized problem u + (H) over bar (x, Du, D(2)u) = 0. Moreover we describe a numerical scheme for the approximation of the effective nonlinearity (H) over bar and we estimate the corresponding rate of convergence.
Rates of convergence in periodic homogenization of fully nonlinear uniformly elliptic PDEs / Camilli, Fabio; Claudio, Marchi. - In: NONLINEARITY. - ISSN 0951-7715. - STAMPA. - 22:6(2009), pp. 1481-1498. [10.1088/0951-7715/22/6/011]
Rates of convergence in periodic homogenization of fully nonlinear uniformly elliptic PDEs
CAMILLI, FABIO;
2009
Abstract
We consider periodic homogenization of the fully nonlinear uniformly elliptic equation u(epsilon) + H(x, x/epsilon, Du(epsilon), D(2)u(epsilon)) = 0. We give an estimate of the rate of convergence of ue to the solution u of the homogenized problem u + (H) over bar (x, Du, D(2)u) = 0. Moreover we describe a numerical scheme for the approximation of the effective nonlinearity (H) over bar and we estimate the corresponding rate of convergence.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
