Nodal Sets and Doubling Conditions in Elliptic Homogenization

Fanghua Lin, Zhongwei Shen

Research output: Contribution to journalArticle

Abstract

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 (US)
Pages (from-to)815-831
Number of pages17
JournalActa Mathematica Sinica, English Series
Volume35
Issue number6
DOIs
StatePublished - Jun 1 2019

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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