Perturbed Obstacle Problems in Lipschitz Domains: Linear Stability and Nondegeneracy in Measure

Authors

Ivan Blank
Jeremy LeCrone, University of RichmondFollow

DOI

10.1216/RMJ-2019-49-5-1407

Abstract

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.

Document Type

Article

Publication Date

2019

Publisher Statement

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.

Recommended Citation

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.