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Stability estimate for the multidimensional elliptic obstacle problem with respect to the obstacle function

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Title: Stability estimate for the multidimensional elliptic obstacle problem with respect to the obstacle function

Authors: Naveed Ahmad, Malkhaz Shashiashvili

Journal: Journal of Prime Research in Mathematics

HEC Recognition History
Category From To
Y 2023-07-01 2024-09-30
Y 2022-07-01 2023-06-30
Y 2021-07-01 2022-06-30
Y 2020-07-01 2021-06-30

Publisher: Abdus Salam School of Mathematical Sciences, GC University

Country: Pakistan

Year: 2012

Volume: 1

Issue: 1

Language: English

Keywords: multidimensional elliptic obstacle problemstability estimateobstacle function

Categories
Optimization (992) Stability Theory (7) Elliptic Equations (1) Partial Differential Equations (47) Mathematics (5170)

Abstract

The stability estimate of the energy integral established by Danelia, Dochviri and Shashiashvili [1] for the solution of the multidimensional obstacle problem in case of the Laplace operator is generalized to the case of arbitrary linear second order self-adjoint elliptic operator. This estimate asserts that if two obstacle functions are close in the \(L^{∞}\)-norm, then the gradients of the solutions of the corresponding obstacle problem are close in the weighted \(L^{2}\) -norm.

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