Liouville's equation

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Liouville's equation

in first arose in the problem of prescribing scalar curvature on a surface. It can be explicitly solved as

as was first observed by Liouville.

It is a limiting case of the sinh-gordon equation.

Standard energy methods give GWP in H^1.

See also

References

  1. J. Liouville, Sur l'equation aux differences partielles , J. Math. Pure Appl. 18(1853), 71--74.