Kruegel, Florian (2015). SOME PROPERTIES OF MINIMIZERS OF A VARIATIONAL PROBLEM INVOLVING THE TOTAL VARIATION FUNCTIONAL. Commun. Pure Appl. Anal, 14 (1). S. 341 - 361. SPRINGFIELD: AMER INST MATHEMATICAL SCIENCES-AIMS. ISSN 1553-5258
Full text not available from this repository.Abstract
The variational problem of minimizing the functional u bar right arrow integral(Omega)vertical bar Du vertical bar+ 1/p integral(Omega) vertical bar Du vertical bar(p) - integral(Omega) au on a domain Omega subset of R-2 under zero boundary values, which among other things models the laminar flow of a Bingham fluid, shows an interesting phenomenon: its minimizer has a maximum set with positive measure (a plateau). In this work we show properties of the minimizer and its plateau, most notably, connectedness and a lower bound of its measure. In addition we look at the related boundary value problem where a = 0, Omega is a convex ring, and two boundary values are given. For this problem we show various results, including quasiconcavity of the minimizer and regularity.
| Item Type: | Journal Article | ||||||||
| Creators: |
|
||||||||
| URN: | urn:nbn:de:hbz:38-417705 | ||||||||
| DOI: | 10.3934/cpaa.2015.14.341 | ||||||||
| Journal or Publication Title: | Commun. Pure Appl. Anal | ||||||||
| Volume: | 14 | ||||||||
| Number: | 1 | ||||||||
| Page Range: | S. 341 - 361 | ||||||||
| Date: | 2015 | ||||||||
| Publisher: | AMER INST MATHEMATICAL SCIENCES-AIMS | ||||||||
| Place of Publication: | SPRINGFIELD | ||||||||
| ISSN: | 1553-5258 | ||||||||
| Language: | English | ||||||||
| Faculty: | Unspecified | ||||||||
| Divisions: | Unspecified | ||||||||
| Subjects: | no entry | ||||||||
| Uncontrolled Keywords: |
|
||||||||
| URI: | http://kups.ub.uni-koeln.de/id/eprint/41770 |
Downloads
Downloads per month over past year
Altmetric
Export
Actions (login required)
 |
View Item |