Communications in Analysis and Geometry

Volume 13 (2005)

Number 1

Asymptotic Morse Theory for the Delta-V Equation

Pages: 187 – 252



Sagun Chanillo

Andrea Malchiodi


Given a smooth bounded domain, we consider the delta-v equation. 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 in [9].

Published 1 January 2005