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The '''DBAR problem''' is the problem of solving the [[differential equation]]

::<math>\bar{\partial} f (z,\bar{z}) = g(z)</math>

for the function <math>f(z,\bar{z})</math>, where <math>g(z)</math> is assumed to be known and <math>z=x+iy</math> is a complex number in a [[Domain (mathematical analysis)|domain]] <math>R\subseteq \mathbb{C}</math>. The operator <math>\bar{\partial}</math> is called the DBAR operator

::<math>\bar{\partial} = \frac{1}{2} \left(\frac{\partial}{\partial x} + i \frac{\partial}{\partial y} \right)</math>

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

::<math>\partial=\frac{\partial}{\partial z}=\frac{1}{2} \left(\frac{\partial}{\partial x} - i \frac{\partial}{\partial y} \right)</math>

denoting the usual differentiation in the complex <math>z</math>-plane.

The DBAR problem is of key importance in the theory of [[integrable systems]]<ref>{{cite web|last=Konopelchenko|first=B. G.|title=On dbar-problem and integrable equations|url=http://arxiv.org/pdf/nlin/0002049v1.pdf|accessdate=3 November 2012}}</ref>  and generalizes the [[Riemann–Hilbert problem]].

==References==
{{Reflist}}

[[Category:Integrable systems|DBAR problem]]