DBAR problem

The DBAR problem is the problem of solving the differential equation

for the function f ( z , z ¯ ) , where g ( z ) is assumed to be known and z = x + i y is a complex number in a domain R ⊆ C . The operator ∂ ¯ is called the DBAR operator

The DBAR operator is nothing other than the complex conjugate of the operator

denoting the usual differentiation in the complex z -plane.

The DBAR problem is of key importance in the theory of integrable systems and generalizes the Riemann–Hilbert problem.