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 language | English (US) |
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Pages (from-to) | 815-831 |
Number of pages | 17 |
Journal | Acta Mathematica Sinica, English Series |
Volume | 35 |
Issue number | 6 |
DOIs | |
State | Published - Jun 1 2019 |
Keywords
- 35B27
- 35J15
- Nodal sets
- doubling condition
- homogenization
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics