Usted está aquí: Existence of solutions to a pure critical elliptic system in a bounded domain

# Existence of solutions to a pure critical elliptic system in a bounded domain

Ponente: Jorge Faya
Institución: IM UNAM
Tipo de Evento: Investigación
Cuándo 17/04/2018 de 11:00 a 12:00 Salón Graciela Salicrup vCal iCal

We consider the weakly coupled critical elliptic system
\label{eq:system}
\begin{cases}
-\Delta u=\mu_{1}|u|^{2^{*}-2}u+\lambda\alpha |u|^{\alpha-2}|v|^{\beta}u & \text{in }\Omega,\\
-\Delta v=\mu_{2}|v|^{2^{*}-2}v+\lambda\beta |u|^{\alpha}|v|^{\beta-2}v & \text{in }\Omega,\\
u=v=0 & \text{on }\partial\Omega,
\end{cases}

where $$\Omega$$ is either a bounded smooth domain in $$\mathbb{R}^{N}$$ or $$\Omega=\mathbb{R}^{N}$$, $$N\geq 3$$, $$2^{*}:=\frac{2N}{N-2}$$ is the critical Sobolev exponent, $$\mu_{1},\mu_{2}>0$$, $$\lambda\in\mathbb{R}$$, $$\alpha, \beta>1$$ and $$\alpha+\beta =2^{*}$$.
This type of systems arises, e.g., in the Hartree-Fock theory for double condensates, that is, Bose-Einstein condensates of two different hyperfine states which overlap in space.

We shall present some existence and multiplicity results for this problem on symmetric domains.
This is joint work with Mónica Clapp