Minimal surface equation
From DispersiveWiki
The (hyperbolic) minimal surface equation takes the form
![\partial_\alpha [ (1 + \phi_\beta \phi^\beta )^{-1/2} \phi_\alpha ] = 0](/wiki/images/math/6/0/f/60f19b1d211cf5ce7129eb67158bef7d.png)
where φ is a scalar function on 
(the graph of a surface in 
). This is the Minkowski analogue of the minimal surface equation in Euclidean space, see Hp1994.
- This is a quasilinear wave equation, and so LWP in Hs for s > n / 2 + 1 follows from energy methods, with various improvements via Strichartz possible. However, it is likely that the special structure of this equation allows us to do better.
- GWP for small smooth compactly supported data is in Lb-p.
