Stochastic homogenization of L variational problems

Scott Armstrong, Panagiotis E. Souganidis

Research output: Contribution to journalArticle

Abstract

We present a homogenization result for L variational problems in general stationary ergodic random environments. By introducing a generalized notion of distance function (a special solution of an associated eikonal equation) and demonstrating a connection to absolute minimizers of the variational problem, we obtain the homogenization result as a consequence of the fact that the latter homogenizes in random environments.

Original languageEnglish (US)
Pages (from-to)3508-3535
Number of pages28
JournalAdvances in Mathematics
Volume229
Issue number6
DOIs
StatePublished - Apr 1 2012

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Stochastic Homogenization
Random Environment
Variational Problem
Homogenization
Eikonal Equation
Distance Function
Minimizer

Keywords

  • Eikonal equation
  • Hamilton-Jacobi equation
  • L calculus of variations
  • Stochastic homogenization

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Stochastic homogenization of L variational problems. / Armstrong, Scott; Souganidis, Panagiotis E.

In: Advances in Mathematics, Vol. 229, No. 6, 01.04.2012, p. 3508-3535.

Research output: Contribution to journalArticle

Armstrong, Scott ; Souganidis, Panagiotis E. / Stochastic homogenization of L variational problems. In: Advances in Mathematics. 2012 ; Vol. 229, No. 6. pp. 3508-3535.
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