Homogenization of the oscillating Dirichlet boundary condition in general domains

被引：16

作者：

Feldman, William M. ^{[1
]}

机构：

[1] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90024 USA

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2014年 / 101卷 / 05期

关键词：

Homogenization; Discontinuous boundary data; Fully nonlinear elliptic equations; Boundary layers; PARTIAL-DIFFERENTIAL-EQUATIONS; VISCOSITY SOLUTIONS; PERIODIC HOMOGENIZATION;

D O I：

10.1016/j.matpur.2013.07.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the homogenization of the Dirichlet problem for fully nonlinear uniformly elliptic operators with periodic oscillation in the operator and in the boundary condition for a general class of smooth bounded domains. This extends the previous results of Barles and Mironescu (2012) [4] in half spaces. We show that homogenization holds despite a possible lack of continuity in the homogenized boundary data. The proof is based on a comparison principle with partial Dirichlet boundary data which is of independent interest. (C) 2013 Elsevier Masson SAS. All rights reserved.

引用

页码：599 / 622

页数：24

共 21 条

[1]

[Anonymous], 1995, Fully nonlinear elliptic equations

[2] Long time averaged reflection force and homogenization of oscillating Neumann boundary conditions [J].

Arisawa, M .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2003, 20 (02) :293-332

[3] Singular Solutions of Fully Nonlinear Elliptic Equations and Applications [J].

Armstrong, Scott N. ;

Sirakov, Boyan ;

Smart, Charles K. .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2012, 205 (02) :345-394

[4] EXIT TIME PROBLEMS IN OPTIMAL-CONTROL AND VANISHING VISCOSITY METHOD [J].

BARLES, G ;

PERTHAME, B .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1988, 26 (05) :1133-1148

[5] Ergodic Problems and Periodic Homogenization for Fully Nonlinear Equations in Half-space Type Domains with Neumann Boundary Conditions [J].

Barles, G. ;

Da Lio, F. ;

Lions, P-L. ;

Souganidis, P. E. .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2008, 57 (05) :2355-2375

[6]

Barles G., 2012, HOMOGENIZATION PROBL

[7]

Bensoussan A., 1978, Asymptotic analysis for periodic structures

[8] Homogenization of fully nonlinear, uniformly elliptic and parabolic partial differential equations in stationary ergodic media [J].

Caffarelli, LA ;

Souganidis, PE ;

Wang, L .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2005, 58 (03) :319-361

[9]

Choi S., 2013, HOMOGENIZATION NONLI

[10] HOMOGENIZATION OF NEUMANN BOUNDARY DATA WITH FULLY NONLINEAR OPERATOR [J].

Choi, Sunhi ;

Kim, Inwon C. ;

Lee, Ki-Ahm .

ANALYSIS & PDE, 2013, 6 (04) :951-972

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