NEUMANN HOMOGENIZATION VIA INTEGRO-DIFFERENTIAL OPERATORS

作者：Guillen Nestor^*; Schwab Russell W^*

来源：Discrete and Continuous Dynamical Systems, 2016, 36(7): 3677-3703.

DOI：10.3934/dcds.2016.36.3677

• Dirichlet to Neumann
• homogenization
• integro-differential representation
• nonlocal boundary operators

In this note we describe how the Neumann homogenization of fully nonlinear elliptic equations can be recast as the study of nonlocal (integro-differential) equations involving elliptic integro-differential operators on the boundary. This is motivated by a new integro-differential representation for nonlinear operators with a comparison principle which we also introduce. In the simple case that the original domain is an in finite strip with almost periodic Neumann data, this leads to an almost periodic homogenization problem involving a fully nonlinear integro-differential operator on the Neumann boundary. This method gives a new proof-which was left as an open question in the earlier work of Barles-DaLio-Lions-Souganidis (2008)-of the result obtained recently by Choi-Kim-Lee (2013), and we anticipate that it will generalize to other contexts.

• 出版日期2016-7