Homogenization of fully nonlinear elliptic equations with oscillating dirichlet boundary data

Ki-ahm Lee; Minha Yoo

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arXiv · 1304.7070

Homogenization of fully nonlinear elliptic equations with oscillating dirichlet boundary data

Ki-ahm Lee·Minha Yoo

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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 $\bar u(x)$ uniformly on every compact subset $K$ of the domain $D$. Moreover, $\bar u$ 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 $\Lambda / \lambda$ is sufficiently large.

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BibTeX RIS

Ki-ahm Lee, Minha Yoo. 2013-04-26. Homogenization of fully nonlinear elliptic equations with oscillating dirichlet boundary data. https://arxiv.org/abs/1304.7070

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