On Second Order Elliptic Equations with a Small Parameter

Mark Freidlin, Wenqing Hu

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

The Neumann problem with a small parameter (Formula presented.) is considered in this paper. The operators L0and L1are self-adjoint second order operators. We assume that L0has a non-negative characteristic form and L1is strictly elliptic. The reflection is with respect to inward co-normal unit vector γε(x). The behavior of limε↓0uε(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.

Original languageEnglish (US)
Pages (from-to)1712-1736
Number of pages25
JournalCommunications in Partial Differential Equations
Volume38
Issue number10
DOIs
StatePublished - Oct 1 2013

Keywords

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

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