Stochastic homogenization of quasilinear Hamilton-Jacobi equations and geometric motions

Scott Armstrong, P. Cardaliaguet

Research output: Contribution to journalArticle

Abstract

We study random homogenization of second-order, degenerate and quasilinear Hamilton-Jacobi equations which are positively homogeneous in the gradient. Included are the equations of forced mean curvature motion and others describing geometric motions of level sets as well as a large class of viscous, nonconvex Hamilton-Jacobi equations. The main results include the first proof of qualitative stochastic homogenization for such equations. We also present quantitative error estimates which give an algebraic rate of homogenization.

Original languageEnglish (US)
Pages (from-to)797-864
Number of pages68
JournalJournal of the European Mathematical Society
Volume20
Issue number4
DOIs
StatePublished - Jan 1 2018

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Stochastic Homogenization
Quasilinear Equations
Hamilton-Jacobi Equation
Homogenization
Motion
Mean Curvature
Level Set
Error Estimates
Gradient

Keywords

  • Error estimate
  • Hamilton-Jacobi equation
  • Mean curvature equation
  • Stochastic homogenization

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Stochastic homogenization of quasilinear Hamilton-Jacobi equations and geometric motions. / Armstrong, Scott; Cardaliaguet, P.

In: Journal of the European Mathematical Society, Vol. 20, No. 4, 01.01.2018, p. 797-864.

Research output: Contribution to journalArticle

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