Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

The constrained least gradient problem in $\textbf {R}^ n$
HTML articles powered by AMS MathViewer

by Peter Sternberg, Graham Williams and William P. Ziemer PDF
Trans. Amer. Math. Soc. 339 (1993), 403-432 Request permission

Abstract:

We consider the constrained least gradient problem \[ \inf \left \{ {\int _\Omega {|\nabla u|dx:u \in {C^{0,1}}(\bar \Omega ),\quad |\nabla u| \leq 1\;{\text {a.e.}},u = g\;{\text {on}}\;\partial \Omega } } \right \}\] which arises as the relaxation of a nonconvex problem in optimal design. We establish the existence of a solution by an explicit construction in which each level set is required to solve an obstacle problem. We also establish the uniqueness of solutions and discuss their structure.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 49Q20
  • Retrieve articles in all journals with MSC: 49Q20
Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 339 (1993), 403-432
  • MSC: Primary 49Q20
  • DOI: https://doi.org/10.1090/S0002-9947-1993-1126213-2
  • MathSciNet review: 1126213