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2019 Perturbed obstacle problems in Lipschitz domains: linear stability and nondegeneracy in measure
Ivan Blank, Jeremy LeCrone
Rocky Mountain J. Math. 49(5): 1407-1418 (2019). DOI: 10.1216/RMJ-2019-49-5-1407

Abstract

We consider the classical obstacle problem on bounded, connected Lipschitz domains $D \subset \mathbb R^n$. 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 $L^1$-norm of perturbations in the data.

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Ivan Blank. Jeremy LeCrone. "Perturbed obstacle problems in Lipschitz domains: linear stability and nondegeneracy in measure." Rocky Mountain J. Math. 49 (5) 1407 - 1418, 2019. https://doi.org/10.1216/RMJ-2019-49-5-1407

Information

Published: 2019
First available in Project Euclid: 19 September 2019

zbMATH: 07113694
MathSciNet: MR4010568
Digital Object Identifier: 10.1216/RMJ-2019-49-5-1407

Subjects:
Primary: 35B20, 35J15, 35R35
Secondary: 31B10, 35J08, 35J25

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.49 • No. 5 • 2019
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