Seminario Geometría (Virtual): Classification of solutions to the critical p-Laplace equations

  • Día: 6 de Noviembre de 2020
  • Hora: 11:30 – 12:30
  • Lugar: Videoconferencia Sala EUROPA de la UGR, en Sala EUROPA de la UGR (Acceso Sala Virtual Europa)
    Contraseña de la reunión: 237948.
  • Ponente: Alberto Roncoroni (Universidad de Granada, España)

Resumen:

We consider the following critical p-Laplace equation:

(1)Δpu+up∗−1=0 in Rn

with n≥2 and 1<p<n. Equation (1) has been largely studied in the PDE’s and geometric analysis’ communities, since extremals of Sobolev inequality solve (1) and, for p=2, the equation is related to the Yamabe’s problem. In particular, it has been recently shown, exploiting the moving planes method, that positive solutions to (1) such that

u∈Lp∗(Rn) and ∇u∈Lp(Rn)

can be completely classified. In the talk we will consider the anisotropic critical p-Laplace equation in convex cones of Rn. Since the moving plane method strongly relies on the symmetries of the equation and of the domain, in the talk a different approach to this problem will be presented. In particular this approach gives a complete classification of the solutions in an anisotropic setting. More precisely, we characterize solutions to the critical p-Laplace equation induced by a smooth norm inside any convex cone of Rn.

This is a joint work with G. Ciraolo and A. Figalli.

Alba Morquecho Delgado
iemath@ugr.es
Gerencia del Instituto de Matemáticas IEMath-GR