Title

An abstract framework for elliptic inverse problems: Part 1. An output least-squares approach

Authors

Mark Gockenbach, Michigan Technological UniversityFollow
Akhtar A. Khan, Michigan Technological University

Document Type

Article

Publication Date

6-1-2007

Abstract

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.

Publisher's Statement

Copyright 2007 SAGE Publications. Publisher's version of record: https://doi.org/10.1177/1081286505055758

Publication Title

Mathematics and Mechanics of Solids

Recommended Citation

Gockenbach, M., & Khan, A. A. (2007). An abstract framework for elliptic inverse problems: Part 1. An output least-squares approach. Mathematics and Mechanics of Solids, 12(3), 259-276. http://doi.org/10.1177/1081286505055758
Retrieved from: https://digitalcommons.mtu.edu/math-fp/12