Doubling inequalities and nodal sets in periodic elliptic homogenization

Document Type

Article

Publication Date

1-1-2022

Abstract

We prove explicit doubling inequalities and obtain uniform upper bounds (under (Formula presented.) -dimensional Hausdorff measure) of nodal sets of weak solutions for a family of linear elliptic equations with rapidly oscillating periodic coefficients. The doubling inequalities, explicitly depending on the doubling index, are proved at different scales by a combination of convergence rates, a three-ball inequality from certain “analyticity,” and a monotonicity formula of a frequency function. The upper bounds of nodal sets are shown by using the doubling inequalities, approximations by harmonic functions and an iteration argument.

Publication Source (Journal or Book title)

Communications in Partial Differential Equations

First Page

549

Last Page

584

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