Homogenization of fully nonlinear elliptic equations with oscillating dirichlet boundary data

2013/04/26 by Ki-Ahm Lee, Lee, Ki-ahm, Minha Yoo +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1304.7070

Abstract

This paper deals with the homogenization of fully nonlinear second order equation with an oscillating Dirichlet boundary data when the operator and boundary data are \e-periodic. We will show that the solution u_\e converges to some function u(x) uniformly on every compact subset K of the domain D. Moreover, u is a solution to some boundary value problem. For this result, we assume that the boundary of the domain has no (rational) flat spots and the ratio of elliptic constants Λ/ λ is sufficiently large.

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