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 {Le} 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 Le(ue) = 0 in a ball in ℝd are bounded uniformly in e > 0. The proof relies on a uniform doubling condition and approximation of ue by solutions of the homogenized equation.
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