Existence and partial regularity results for the gradient flow for a variational functional of degenerate type
We establish the existence and partial regularity of a weak solution to the evolution problem associated to a variational functional of degenerate type. We use the penalty method due to Chen and Struwe to make approximation of solutions. The main ingredient is to show that the ≤-regularity theorem h...
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| Format: | Article |
| Language: | English |
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Sapienza Università Editrice
1999-01-01
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| Series: | Rendiconti di Matematica e delle Sue Applicazioni |
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| Online Access: | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/1999(3)/317-351.pdf |
| _version_ | 1828219703425761280 |
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| author | Masashi Misawa |
| author_facet | Masashi Misawa |
| author_sort | Masashi Misawa |
| collection | DOAJ |
| description | We establish the existence and partial regularity of a weak solution to the evolution problem associated to a variational functional of degenerate type. We use the penalty method due to Chen and Struwe to make approximation of solutions. The main ingredient is to show that the ≤-regularity theorem holds uniformly for approximating solutions. For this purpose, we derive the monotonicity formula using the quadratic growth of the energy density at infinity. We also obtain the Bochner formula in somewhat technical way and take some cares to derive the Harnack estimate from it. |
| first_indexed | 2024-04-12T16:18:58Z |
| format | Article |
| id | doaj.art-2b77a05f372843a3b742e00ca200555d |
| institution | Directory Open Access Journal |
| issn | 1120-7183 2532-3350 |
| language | English |
| last_indexed | 2024-04-12T16:18:58Z |
| publishDate | 1999-01-01 |
| publisher | Sapienza Università Editrice |
| record_format | Article |
| series | Rendiconti di Matematica e delle Sue Applicazioni |
| spelling | doaj.art-2b77a05f372843a3b742e00ca200555d2022-12-22T03:25:38ZengSapienza Università EditriceRendiconti di Matematica e delle Sue Applicazioni1120-71832532-33501999-01-01193317351Existence and partial regularity results for the gradient flow for a variational functional of degenerate typeMasashi Misawa0The University of Electro-CommunicationsWe establish the existence and partial regularity of a weak solution to the evolution problem associated to a variational functional of degenerate type. We use the penalty method due to Chen and Struwe to make approximation of solutions. The main ingredient is to show that the ≤-regularity theorem holds uniformly for approximating solutions. For this purpose, we derive the monotonicity formula using the quadratic growth of the energy density at infinity. We also obtain the Bochner formula in somewhat technical way and take some cares to derive the Harnack estimate from it.https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/1999(3)/317-351.pdfdegenerate parabolic systemp-harmonic mapgradient flow |
| spellingShingle | Masashi Misawa Existence and partial regularity results for the gradient flow for a variational functional of degenerate type Rendiconti di Matematica e delle Sue Applicazioni degenerate parabolic system p-harmonic map gradient flow |
| title | Existence and partial regularity results for the gradient flow for a variational functional of degenerate type |
| title_full | Existence and partial regularity results for the gradient flow for a variational functional of degenerate type |
| title_fullStr | Existence and partial regularity results for the gradient flow for a variational functional of degenerate type |
| title_full_unstemmed | Existence and partial regularity results for the gradient flow for a variational functional of degenerate type |
| title_short | Existence and partial regularity results for the gradient flow for a variational functional of degenerate type |
| title_sort | existence and partial regularity results for the gradient flow for a variational functional of degenerate type |
| topic | degenerate parabolic system p-harmonic map gradient flow |
| url | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/1999(3)/317-351.pdf |
| work_keys_str_mv | AT masashimisawa existenceandpartialregularityresultsforthegradientflowforavariationalfunctionalofdegeneratetype |