Advanced Search

Journal Navigation

Journal Home

Subscriptions

Archive

Contact Us

Table of Contents

Sign In to gain access to subscriptions and/or personal tools.
Mathematics and Mechanics of Solids
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
1081286505055758v1
12/3/259    most recent
Right arrow References
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Add to Saved Citations
Right arrow Download to citation manager
Right arrowRequest Permissions
Right arrow Request Reprints
Right arrow Add to My Marked Citations
Citing Articles
Right arrow Citing Articles via HighWire
Right arrow Citing Articles via Web of Science (2)
Right arrow Citing Articles via Google Scholar
Right arrow Citing Articles via Scopus
Google Scholar
Right arrow Articles by Gockenbach, M. S.
Right arrow Articles by Khan, A. A.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Complore   Add to Connotea   Add to Del.icio.us   Add to Digg   Add to Reddit   Add to Technorati   Add to Twitter  
What's this?

An Abstract Framework for Elliptic Inverse Problems: Part 1. An Output Least-Squares Approach

Mark S. Gockenbach

Department of Mathematical Sciences, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931-1295, USA

Akhtar A. Khan

Department of Mathematical Sciences, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931-1295, USA

The solution of an elliptic boundary value problem is an infinitely differentiable function of the coefficient in the partial differential equation. When the (coefficient-dependent) energy norm is used, the result is a smooth, convex output least-squares functional. Using total variation regularization, it is possible to estimate discontinuous coefficients from interior measurements. The minimization problem is guaranteed to have a solution, which can be obtained in the limit from finite-dimensional discretizations of the problem. These properties hold in an abstract framework that encompasses several interesting problems: the standard (scalar) elliptic BVP in divergence form, the system of isotropic elasticity, and others.

Key Words: Total variation regularization • distributed parameter estimation • Lamé parameters

This version was published on June 1, 2007

Mathematics and Mechanics of Solids, Vol. 12, No. 3, 259-276 (2007)
DOI: 10.1177/1081286505055758
Add to CiteULike CiteULike   Add to Complore Complore   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us   Add to Digg Digg   Add to Reddit Reddit   Add to Technorati Technorati   Add to Twitter Twitter    What's this?


This article has been cited by other articles:


Home page
 Mathematics and Mechanics of SolidsHome page
M. S. Gockenbach and A. A. Khan
An Abstract Framework for Elliptic Inverse Problems: Part 2. An Augmented Lagrangian Approach
Mathematics and Mechanics of Solids, August 1, 2009; 14(6): 517 - 539.
[Abstract] [PDF]