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

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

2002-05-10

arxiv.org/abs/math/0205106v1

Comm. in Analysis and Geometry, vol. 13(1)(2005), 187-251.

Mathematics

Analysis of PDEs

Scientific paper

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