The time-like minimal surface equation in Minkowski space: low regularity solutions
| Autor: | Ai, Albert, Ifrim, Mihaela, Tataru, Daniel |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | It has long been conjectured that for nonlinear wave equations which satisfy a nonlinear form of the null condition, the low regularity well-posedness theory can be significantly improved compared to the sharp results of Smith-Tataru for the generic case. The aim of this article is to prove the first result in this direction, namely for the time-like minimal surface equation in the Minkowski space-time. Further, our improvement is substantial, namely by $3/8$ derivatives in two space dimensions and by $1/4$ derivatives in higher dimensions. Comment: 120 pages, minor typos corrected |
| Databáze: | arXiv |
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