DBAR problem

The DBAR problem, or the

∂ ¯

-problem, is the problem of solving the differential equation

for the function

is assumed to be known and

is a complex number in a domain

The operator

is called the DBAR operator:[1]

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

denoting the usual differentiation in the complex

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