Vol. 6, No. 4, 2013

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Homogenization of Neumann boundary data with fully nonlinear operator

Sunhi Choi, Inwon C. Kim and Ki-Ahm Lee

Vol. 6 (2013), No. 4, 951–972
Abstract

In this paper we study periodic homogenization problems for solutions of fully nonlinear PDEs in half-spaces with oscillatory Neumann boundary data. We show the existence and uniqueness of the homogenized Neumann data for a given half-space. Moreover, we show that there exists a continuous extension of the homogenized slope as the normal of the half-space varies over “irrational” directions.

Keywords
homogenization, boundary layer, fully nonlinear elliptic PDE, viscosity solutions, Neumann boundary data
Mathematical Subject Classification 2010
Primary: 35B27, 35J25, 35J60
Milestones
Received: 12 December 2011
Revised: 13 December 2011
Accepted: 1 September 2012
Published: 21 August 2013
Authors
Sunhi Choi
Department of Mathematics
University of Arizona
Tucson, AZ 85721
United States
Inwon C. Kim
Department of Mathematics
University of California at Los Angeles
Los Angeles, CA 90095
United States
Ki-Ahm Lee
School of Mathematical Sciences
Seoul National University
Seoul 151-747
South Korea