Published Paper

Inserted: 27 nov 2024
Last Updated: 27 nov 2024

Journal: Rend. Lincei Mat. Appl.
Volume: 33
Pages: 967-995
Year: 2022
Doi: DOI 10.4171/RLM/995

Abstract:

In this survey, we consider the sharp Sobolev inequality in convex cones. We also prove it by using the optimal transport technique. Then we present some results related to the Euler-Lagrange equation of the Sobolev inequality: the so-called critical p-Laplace equation. Finally, we discuss some stability results related to the Sobolev inequality.