Center for                           Nonlinear Analysis
CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact
Seminar Abstracts

## Michal Kowalczyk, Universidad de Chile

"Critical points of the regular part of the harmonic Green's function with Robin boundary condition"

Abstract: In this talk I will consider the Green's function for the Laplacian in a smooth bounded domain $\Omega \subset R^N$ with Robin boundary condition $$\pd{G_{\lambda}{\nu} + \lambda b(x) G_{\lambda} = 0, \quad \mbox{on} \ \partial \Omega,$$ and its regular part $S_{\lambdd}(x,y)$, where $b>0$ is smooth. I will show that in general, as $\lambda \to \infty$, the Robin function $R_{\lambda}(x) = S_{\lambda}(x,x)$ has at least 3 critical points. Moreover, in the case $b\equiv const$, $R_{\lambda}$ has critical points near non-degenerate critical points of the mean curvature of the boundary, and when $b \not\equiv const$ there are critical points of $b$. I will discuss applications of these results in the context of concentration phenomena for elliptic singular perturbation problems. This is a joint work with J. D. Davila and M. Montenegro.

TUESDAY, SEPTEMBER 11, 2007
Time: 1:30 P.M.
Location: PPB 300