DBAR problem

The DBAR problem, or the formula_1-problem, is the problem of solving the differential equation
for the function formula_3, where formula_4 is assumed to be known and formula_5 is a complex number in a domain formula_6. The operator formula_1 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 formula_10-plane.
The DBAR problem is of key importance in the theory of integrable systems and generalizes the Riemann–Hilbert problem.