Cambiar a contenido. | Saltar a navegación

Herramientas Personales
Entrar

Navegación

Usted está aquí: Inicio / Actividades / Seminarios / Seminario de Ecuaciones Diferenciales No Lineales (SEDNOL) / Actividades del Seminario de Ecuaciones Diferenciales No Lineales / Towers of Nodal Bubbles for the Bahri-Coron Problem in Punctured Domains

Towers of Nodal Bubbles for the Bahri-Coron Problem in Punctured Domains

Ponente: Jorge Faya
Institución: Universidad de Chile
Tipo de Evento: Investigación
Cuándo 24/08/2017
de 11:00 a 12:00
Dónde Por definir
Agregar evento al calendario vCal
iCal

 Let $\Omega$ be a smooth bounded domain in $\mathbb{R}^{N}$ which contains a ball centered at the origin. Consider   problem
 \begin{equation}\label{1}
 (\wp_{\delta})\qquad\left\{
 \begin{array}
 [c]{ll}%
 -\Delta u=|u|^{ 2^{*}- 2}u & \text{in }\Omega_{\delta},\\[3mm]
 u=0 & \text{on }\partial\Omega_{\delta},\\
 \end{array}
 \right.
 \end{equation}
 here   $N\geq 3$,   $2^{*}=\frac{2N}{N-2}$ is the critical Sobolev exponent and $\Omega_{\delta}:=\{x\in\Omega: |x|>\delta \}$. In this talk we will discuss the existence of nodal solutions $(u_{m, \delta})$ for problem $(\wp_{\delta})$. Moreover, if $\Omega$ is starshaped,   we show that the  solutions $(u_{m, \delta})$  concentrate and blowup at  $0$, as $\delta\rightarrow0$, and their limit profile is a  tower of nodal bubbles, i.e., they are a sum of rescaled nonradial sign-changing solutions to the limit problem
  \begin{equation}\label{1}
  \qquad\left\{
  \begin{array}
  [c]{ll}%
  -\Delta u=|u|^{ 2^{*}- 2}u, & u\in D^{1,2}(\mathbb{R^{N}})\\
  \end{array}
  \right.
  \end{equation}
 centered at the origin.
 
 This is a joint work with M. Clapp and F. Pacella.