Asymptotic Morse theory for the equation $\text{D}v=2v_x\wedge v_y$

Given a smooth bounded domain $\text{O}\subseteq {\mathbb{R}}^2$, we consider the equation $\text{D}v=2v_x\wedge v_y$ in $\text{O}$, where $v:\text{O}\to {\mathbb{R}}^3$. We prescribe Dirichlet boundary datum, and consider the case in which this datum converges to zero. An asymptotic study of the corresponding Euler functional is performed, analyzing multiple-bubbling phenomena. This allows us to settle a particular case of a question raised by H. Brezis and J.M. Coron.