Nodal Sets and Doubling Conditions in Elliptic Homogenization

Fanghua Lin, Zhongwei Shen

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


This paper is concerned with uniform measure estimates for nodal sets of solutions in elliptic homogenization. We consider a family of second-order elliptic operators {L ε } in divergence form with rapidly oscillating and periodic coefficients. We show that the (d-1)-dimensional Hausdorff measures of the nodal sets of solutions to L ε (u ε ) = 0 in a ball in ℝ d are bounded uniformly in ε > 0. The proof relies on a uniform doubling condition and approximation of u ε by solutions of the homogenized equation.

Original languageEnglish
Pages (from-to)815-831
Number of pages17
JournalActa Mathematica Sinica, English Series
Issue number6
StatePublished - Jun 1 2019

Bibliographical note

Funding Information:
Received May 24, 2018, accepted October 26, 2018 The first author is supported in part by NSF (Grant No. DMS-1501000); the second author is supported in part by NSF (Grant No. DMS-1600520)

Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany & The Editorial Office of AMS.


  • 35B27
  • 35J15
  • Nodal sets
  • doubling condition
  • homogenization

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics


Dive into the research topics of 'Nodal Sets and Doubling Conditions in Elliptic Homogenization'. Together they form a unique fingerprint.

Cite this