Stochastic homogenization of viscous Hamilton-Jacobi equations and applications

Scott Armstrong, Hung V. Tran

Research output: Contribution to journalArticle

Abstract

We present stochastic homogenization results for viscous Hamilton-Jacobi equations using a new argument that is based only on the subadditive structure of maximal subsolutions (i.e., solutions of the "metric problem"). This permits us to give qualitative homogenization results under very general hypotheses: in particular, we treat nonuniformly coercive Hamiltonians that satisfy instead a weaker averaging condition. As an application, we derive a general quenched large deviation principle for diffusions in random environments and with absorbing random potentials.

Original languageEnglish (US)
Pages (from-to)1969-2007
Number of pages39
JournalAnalysis and PDE
Volume7
Issue number8
DOIs
StatePublished - 2014

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Stochastic Homogenization
Hamiltonians
Hamilton-Jacobi Equation
Random Potential
Subsolution
Large Deviation Principle
Random Environment
Absorbing
Homogenization
Averaging
Metric

Keywords

  • Degenerate diffusion
  • Diffusion in random environment
  • Hamilton-Jacobi equation
  • Quenched large deviation principle
  • Stochastic homogenization
  • Weak coercivity

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Numerical Analysis

Cite this

Stochastic homogenization of viscous Hamilton-Jacobi equations and applications. / Armstrong, Scott; Tran, Hung V.

In: Analysis and PDE, Vol. 7, No. 8, 2014, p. 1969-2007.

Research output: Contribution to journalArticle

Armstrong, Scott ; Tran, Hung V. / Stochastic homogenization of viscous Hamilton-Jacobi equations and applications. In: Analysis and PDE. 2014 ; Vol. 7, No. 8. pp. 1969-2007.
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