Sesión Geometría, Topología y Teoría de Lie

Hardy-Sobolev equation on riemannian manifolds.

Guillermo Henry

Universidad de Buenos Aires-IMAS, Argentina   -   Esta dirección de correo electrónico está siendo protegida contra los robots de spam. Necesita tener JavaScript habilitado para poder verlo.

Let \((M,g)\) be a closed Riemannian manifold of dimension at least \(3\). Let \(S\) be the union of the focal submanifolds of an isoparametric function on \((M,g)\). In this talk we are going to discuss results on the existence of solutions of the Hardy-Sobolev type equation \[\Delta_g u+K(x)u=\frac{u^{q-1}}{\left(d_{S}(x)\right)^s},\] where \(\Delta_g\) is the Laplace-Beltrami operator, \(d_{S}(x)\) is the distance from \(x\) to \(S\), \(K\) is a continuous function on \(M\) and \(q>2\). In particular, we will prove the existence of infinite sign-changing solutions to this equation.

Trabajo en conjunto con: Jimmy Petean, CIMAT, Guanajuato, México.

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