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- Title
The time-like minimal surface equation in Minkowski space: low regularity solutions.
- Authors
Ai, Albert; Ifrim, Mihaela; Tataru, Daniel
- Abstract
It has long been conjectured that for nonlinear wave equations that 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.
- Subjects
MINKOWSKI space; NONLINEAR wave equations; MINIMAL surfaces; EQUATIONS
- Publication
Inventiones Mathematicae, 2024, Vol 235, Issue 3, p745
- ISSN
0020-9910
- Publication type
Article
- DOI
10.1007/s00222-023-01231-3