On Second Order Elliptic Equations with a Small Parameter

Author

Mark Freidlin
Wenqing Hu, Missouri University of Science and TechnologyFollow

Abstract

The Neumann problem with a small parameter (Formula presented.) is considered in this paper. The operators L₀ and L₁ are self-adjoint second order operators. We assume that L₀ has a non-negative characteristic form and L₁ is strictly elliptic. The reflection is with respect to inward co-normal unit vector γ^ε(x). The behavior of lim _ε↓0 u^ε(x) is effectively described via the solution of an ordinary differential equation on a tree. We calculate the differential operators inside the edges of this tree and the gluing condition at the root. Our approach is based on an analysis of the corresponding diffusion processes.

Recommended Citation

M. Freidlin and W. Hu, "On Second Order Elliptic Equations with a Small Parameter," Communications in Partial Differential Equations, vol. 38, no. 10, pp. 1712 - 1736, Taylor & Francis, Oct 2013.

The definitive version is available at https://doi.org/10.1080/03605302.2013.812658

Department(s)

Mathematics and Statistics

Keywords and Phrases

Averaging principle; Diffusion processes on a graph; Equations with non-negative characteristic form; Second order equations with a small parameter

International Standard Serial Number (ISSN)

0360-5302

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2013 Taylor & Francis, All rights reserved.

Publication Date

01 Oct 2013