Local solvability of a constrainedgradient system of total variation
A 1-harmonic map flow equation, a gradient system of total variation where values of unknowns are constrained in a compact manifold in ℝN, is formulated by the use of subdifferentials of a singular energythe total variation. An abstract convergence result is established to show that solutions of app...
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/S1085337504311048 |
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| _version_ | 1832565221877612544 |
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| author | Yoshikazu Giga Yohei Kashima Noriaki Yamazaki |
| author_facet | Yoshikazu Giga Yohei Kashima Noriaki Yamazaki |
| author_sort | Yoshikazu Giga |
| collection | DOAJ |
| description | A 1-harmonic map flow equation, a gradient system of total variation where values of unknowns are constrained in a compact manifold in ℝN, is formulated by the use of subdifferentials of a singular energythe total variation. An abstract convergence result is established to show that solutions of approximate problem converge to a solution of the limit problem. As an application of our convergence result, a local-in-time solution of 1-harmonic map flow equation is constructed as a limit of the solutions of p-harmonic (p>1) map flow equation, when the initial data is smooth with small total variation under periodic boundary condition. |
| format | Article |
| id | doaj-art-36dd4d3990cb40d2bc9b74d7430023aa |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-36dd4d3990cb40d2bc9b74d7430023aa2025-02-03T01:08:54ZengWileyAbstract and Applied Analysis1085-33751687-04092004-01-012004865168210.1155/S1085337504311048Local solvability of a constrainedgradient system of total variationYoshikazu Giga0Yohei Kashima1Noriaki Yamazaki2Department of Mathematics, Hokkaido University, Sapporo 060-0810, JapanDepartment of Mathematics, Hokkaido University, Sapporo 060-0810, JapanDepartment of Mathematical Science, Common Subject Division, Muroran Institute of Technology, 27-1 Mizumoto-cho, Muroran 050-8585, JapanA 1-harmonic map flow equation, a gradient system of total variation where values of unknowns are constrained in a compact manifold in ℝN, is formulated by the use of subdifferentials of a singular energythe total variation. An abstract convergence result is established to show that solutions of approximate problem converge to a solution of the limit problem. As an application of our convergence result, a local-in-time solution of 1-harmonic map flow equation is constructed as a limit of the solutions of p-harmonic (p>1) map flow equation, when the initial data is smooth with small total variation under periodic boundary condition.http://dx.doi.org/10.1155/S1085337504311048 |
| spellingShingle | Yoshikazu Giga Yohei Kashima Noriaki Yamazaki Local solvability of a constrainedgradient system of total variation Abstract and Applied Analysis |
| title | Local solvability of a constrainedgradient system of total variation |
| title_full | Local solvability of a constrainedgradient system of total variation |
| title_fullStr | Local solvability of a constrainedgradient system of total variation |
| title_full_unstemmed | Local solvability of a constrainedgradient system of total variation |
| title_short | Local solvability of a constrainedgradient system of total variation |
| title_sort | local solvability of a constrainedgradient system of total variation |
| url | http://dx.doi.org/10.1155/S1085337504311048 |
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