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

S. Chanillo·A. Malchiodi
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Abstract

Given a smooth bounded domain $Ø\subseteq \R^2$, we consider the equation $\D v = 2 v_x \wedge v_y$ in $Ø$, where $v: Ø\to \R^3$. 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.

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S. Chanillo, A. Malchiodi. 2002-05-10. Asymptotic Morse theory for the equation $\D v = 2 v_x \wedge v_y$. https://arxiv.org/abs/math/0205106

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