The Principal Eigenvalue for Linear Second Order Elliptic Equations with Natural Boundary Conditions.

Abstract

This paper presents our recent work on the characterization of the principal eigenvalue. We have been able to derive a new characterization of the principal eigenvalue for second order linear elliptic partial differential equations, not necessarily self-adjoint, with both natural and Dirichlet boundary conditions, and also give a new alternative numerical method for calculating both the principal eigenvalue and corresponding eigenvector in the case of natural boundary conditions. Secondly, we report recent progress on determining the asymptotic behavior of the principal eigenvalue for some singularly perturbed eigenvalue problems as a small nuisance parameter tends to zero. The principal eigenvalue is the optimal value for a singularly perturbed stationary stochastic control problem. We are thus able to determine the asymptotic behavior of the optimal value of certain stationary stochastic control problems.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1978
Accession Number
ADA062877

Entities

People

  • Charles J. Holland

Organizations

  • Purdue University

Tags

Communities of Interest

  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Boundaries
  • Brownian Motion
  • Control Theory
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Integral Equations
  • Markov Chains
  • New York
  • Partial Differential Equations
  • Probability
  • Probability Distributions
  • Reflection
  • Security
  • Stationary
  • Stochastic Control

Fields of Study

  • Mathematics

Readers

  • Linear Algebra