DBAR problem

The DBAR problem is the problem of solving the differential equation

for the function ${\displaystyle f(z,{\bar {z}})}$, where ${\displaystyle g(z)}$ is assumed to be known and ${\displaystyle z=x+iy}$ is a complex number in a domain ${\displaystyle R\subseteq \mathbb {C} }$. The operator ${\displaystyle {\bar {\partial }}}$ is called the DBAR operator

...
Wikipedia