28 Novembre, 2014 14:30 in punto

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

PARTIAL DIFFERENTIAL EQUATIONS ON HYPERBOLIC SPACE

DEBDIP GANGULY, POLITECNICO DI TORINO

Aula Seminari III piano

In this talk, semilinear elliptic partial differential equations(PDEs) on hy-perbolic space and related problems will be presented. Several geometric problems lead to the study of the equation:
$$- \Delta _{B ^N} u - \lambda u = |u| ^ {p-2} u , u \in H ^ 1 (B ^N)$$
where $\lambda$ is a real parameter and $H^1(B^N)$ denotes the Sobolev space on the conformal ball model of the hyperbolic space. Some existence, non existence and qualitative properties of solutions of above equation will be pointed out.