The obstacle problem for the total variation flow

Bögelein V, Duzaar F, Scheven C (2016)

Publication Type: Journal article

Publication year: 2016

Journal

Annales Scientifiques De L Ecole Normale Superieure Elsevier Masson

Book Volume: 49

Pages Range: 1143--1188

Journal Issue: 5

DOI: 10.24033/asens.2306

Abstract

We prove existence results for the obstacle problem related to the total variation flow. For sufficiently regular obstacles the solutions are obtained via the method of minimizing movements. The results for more general obstacles are derived by approximation with regular obstacles in the sense of a stability property of solutions with respect to the obstacle. Finally, we present the treatment of the evolutionary counterpart of a classical stationary result concerning minimal surfaces with thin obstacles by means of the (n-1)-dimensional variational measure introduced by De Giorgi, Colombini and Piccinini.

Authors with CRIS profile

Frank Duzaar Lehrstuhl für Partial Differential Equations

Involved external institutions

Universität Duisburg-Essen (UDE) DE Germany (DE) Universität Salzburg (Paris Lodron Universität Salzburg) AT Austria (AT)

How to cite

APA:

Bögelein, V., Duzaar, F., & Scheven, C. (2016). The obstacle problem for the total variation flow. Annales Scientifiques De L Ecole Normale Superieure, 49(5), 1143--1188. https://dx.doi.org/10.24033/asens.2306

MLA:

Bögelein, Verena, Frank Duzaar, and Christoph Scheven. "The obstacle problem for the total variation flow." Annales Scientifiques De L Ecole Normale Superieure 49.5 (2016): 1143--1188.

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