Minimal surface equation

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The (hyperbolic) minimal surface equation takes the form

where 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 for 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.