On Second Order Elliptic Equations with a Small Parameter
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 γε(x). The behavior of lim ε↓0 uε(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.
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
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)
Article - Journal
© 2013 Taylor & Francis, All rights reserved.
01 Oct 2013