We consider the classical obstacle problem on bounded, connected Lipschitz domains D⊂Rn. We derive quantitative bounds on the changes to contact sets under general perturbations to both the right-hand side and the boundary data for obstacle problems. In particular, we show that the Lebesgue measure of the symmetric difference between two contact sets is linearly comparable to the L1-norm of perturbations in the data.

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Copyright © 2019 Rocky Mountain Mathematics Consortium. This article first appeared in Rocky Mountain Journal of Mathematics 49:5 (2019), 1407-1418.

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Citation Example for Article (Chicago):

Blank, Ivan, and Jeremy LeCrone. “Perturbed Obstacle Problems in Lipschitz Domains: Linear Stability and Nondegeneracy in Measure.” Rocky Mountain Journal of Mathematics 49, no. 5 (2019): 1407–418.

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