Name
Abstract | ||
|---|---|---|
Motivated by emerging applications from imaging processing, this paper studies the heat flow of a generalized p-harmonic map into spheres for the whole spectrum, 1 <= p < infinity, in a unified framework. The existence of global weak solutions is established for the flow using the energy method together with a regularization and a penalization technique. In particular, a BV-solution concept is introduced and the existence of such a solution is proved for the 1-harmonic map heat flow. The main idea used to develop such a theory is to exploit the properties of measures of the forms A . del v and A boolean AND del v, which pair a divergence-L-1, or a divergence-measure, tensor field A and a BV-vector field v. Based on these analytical results, a practical fully discrete finite element method is then proposed for approximating weak solutions of the p-harmonic map heat flow, and the convergence of the proposed numerical method is also established. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1137/070680825 | SIAM JOURNAL ON MATHEMATICAL ANALYSIS |
Keywords | DocType | Volume |
p-harmonic maps,heat flow,penalization,energy method,color image denoising,finite element method | Journal | 40 |
Issue | ISSN | Citations |
4 | 0036-1410 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| John W. Barrett | 1 | 284 | 61.65 |
| Xiaobing Feng | 2 | 906 | 112.55 |
| Andreas Prohl | 3 | 302 | 67.29 |