Sharp quantitative stability of Poincaré-Sobolev inequality in the hyperbolic space and applications to fast diffusion flows
Year: 2024
Type: article
Abstract: Consider the Poincaré-Sobolev inequality on the hyperbolic space: for every $$n \ge 3$$ n ≥ 3 and $$1 < p \le \frac{n+2}{n-2},$$ 1 < p ≤ n + 2 n - 2 , there exists a best constant $$S_{n,p, \lambda }({\mathbb {B}}^{n})>0$$ S n , p , λ ( B n ) > 0 such that $$\begin{aligned} S_{n, p, \lambda }({\mathbb {B}}^{n})\left( ~\int \limits _{{\mathbb {B}}^{n}}|u|^{{p+1}} \, \textrm{d}v_{{\mathbb {B}}^n} \right) ^{\frac{2}{p+1}} \le \int \limits _{{\mathbb {B}}^{n}}\left( |\nabla _{{\mathbb {B}}^{n}}u|^{2}-\lambda u^{2}\right) \, \textrm{d}v_{{\mathbb {B}}^n}, \end{aligned}$$ S n , p , λ ( B n ) ∫ B n | u | p + 1 d v B n 2 p + 1 ≤ ∫ B n | ∇ B n u | 2 - λ u 2 d v B n , holds for all $$u\in C_c^{\infty }({\mathbb {B}}^n),$$ u ∈ C c ∞ ( B n )
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4405055641