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

S. Chanillo; A. Malchiodi

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

Analysis of PDEs 2007-05-23 v1 Differential Geometry

Authors: S. Chanillo , A. Malchiodi

Abstract

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.

Keywords

asymptotic morse theory dirichlet boundary euler functional multiple-bubbling brezis-coron problem

Cite

@article{arxiv.math/0205106,
  title  = {Asymptotic Morse theory for the equation $\D v = 2 v_x \wedge v_y$},
  author = {S. Chanillo and A. Malchiodi},
  journal= {arXiv preprint arXiv:math/0205106},
  year   = {2007}
}

Related papers

View all related →