Homogenization of symmetric stable-like processes in stationary ergodic media

Xin Chen, Zhen Qing Chen, Takashi Kumagai, Jian Wang

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

This paper studies homogenization of symmetric nonlocal Dirichlet forms with stable-like jumping kernels in a one-parameter stationary ergodic environment. Under suitable conditions, we establish results of homogenization and identify the limiting effective Dirichlet forms explicitly. The coefficients in the jumping kernels of Dirichlet forms and symmetrizing measures are allowed to be degenerate and unbounded, and the coefficients in the effective Dirichlet forms can also be degenerate.

Original languageEnglish
Pages (from-to)2957-3001
Number of pages45
JournalSIAM Journal on Mathematical Analysis
Volume53
Issue number3
DOIs
Publication statusPublished - 2021
Externally publishedYes

Keywords

  • Ergodic random medium
  • Homogenization
  • Symmetric nonlocal Dirichlet form
  • α-stable-like operator

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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