Homogenization of neumann boundary data with fully nonlinear operator

Sunhi Choi; Inwon C. Kim; Ki Ahm Lee

doi:10.2140/apde.2013.6.951

Homogenization of neumann boundary data with fully nonlinear operator

Sunhi Choi, Inwon C. Kim, Ki Ahm Lee

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

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.

Original language	English (US)
Pages (from-to)	951-972
Number of pages	22
Journal	Analysis and PDE
Volume	6
Issue number	4
DOIs	https://doi.org/10.2140/apde.2013.6.951
State	Published - 2013

Keywords

Boundary layer
Fully nonlinear elliptic PDE
Homogenization
Neumann boundary data
Viscosity solutions

ASJC Scopus subject areas

Analysis
Numerical Analysis
Applied Mathematics

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10.2140/apde.2013.6.951

Cite this

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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 = "Boundary layer, Fully nonlinear elliptic PDE, Homogenization, Neumann boundary data, Viscosity solutions",

author = "Sunhi Choi and Kim, {Inwon C.} and Lee, {Ki Ahm}",

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T1 - Homogenization of neumann boundary data with fully nonlinear operator

AU - Choi, Sunhi

AU - Kim, Inwon C.

AU - Lee, Ki Ahm

PY - 2013

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N2 - 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.

AB - 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.

KW - Boundary layer

KW - Fully nonlinear elliptic PDE

KW - Homogenization

KW - Neumann boundary data

KW - Viscosity solutions

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DO - 10.2140/apde.2013.6.951

M3 - Article

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SN - 2157-5045

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EP - 972

JO - Analysis and PDE

JF - Analysis and PDE

IS - 4

ER -

Homogenization of neumann boundary data with fully nonlinear operator

Abstract

Keywords

ASJC Scopus subject areas

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