Degenerate stability of some Sobolev inequalities
RL Frank - Ann. Inst. H. Poincaré Anal. Non Linéaire, to appear, 2022 - ems.press
We show that on S1. 1= pd 2/Sd1. 1/the conformally invariant Sobolev inequality holds with
a remainder term that is the fourth power of the distance to the optimizers. The fourth power …
a remainder term that is the fourth power of the distance to the optimizers. The fourth power …
The sharp Sobolev inequality and its stability: An introduction
RL Frank - arXiv preprint arXiv:2304.03115, 2023 - arxiv.org
These notes are an extended version of a series of lectures given at the CIME Summer
School in Cetraro in June 2022. The goal is to explain questions about optimal functional …
School in Cetraro in June 2022. The goal is to explain questions about optimal functional …
Degenerate stability of the Caffarelli–Kohn–Nirenberg inequality along the Felli–Schneider curve
RL Frank, JW Peteranderl - Calculus of Variations and Partial Differential …, 2024 - Springer
We show that the Caffarelli–Kohn–Nirenberg (CKN) inequality holds with a remainder term
that is quartic in the distance to the set of optimizers for the full parameter range of the Felli …
that is quartic in the distance to the set of optimizers for the full parameter range of the Felli …
On the stability of critical points of the Hardy-Littlewood-Sobolev inequality
K Liu, Q Zhang, W Zou - arXiv preprint arXiv:2306.15862, 2023 - arxiv.org
This paper is concerned with the quantitative stability of critical points of the Hardy-
Littlewood-Sobolev inequality. Namely, we give quantitative estimates for the Choquard …
Littlewood-Sobolev inequality. Namely, we give quantitative estimates for the Choquard …
Stability of Sobolev inequalities on Riemannian manifolds with Ricci curvature lower bounds
We study the qualitative stability of two classes of Sobolev inequalities on Riemannian
manifolds. In the case of positive Ricci curvature, we prove that an almost extremal function …
manifolds. In the case of positive Ricci curvature, we prove that an almost extremal function …
Sharp quantitative stability of Struwe's decomposition of the Poincar\'e-Sobolev inequalities on the hyperbolic space: Part I
A classical result owing to Mancini and Sandeep [Ann. Sc. Norm. Super. Pisa Cl. Sci. 7
(2008)] asserts that all positive solutions of the Poincar\'e-Sobolev equation on the …
(2008)] asserts that all positive solutions of the Poincar\'e-Sobolev equation on the …
Sharp quantitative rigidity results for maps from to of general degree
M Rupflin - arXiv preprint arXiv:2305.17045, 2023 - arxiv.org
As the energy of any map $ v $ from $ S^ 2$ to $ S^ 2$ is at least $4\pi\vert deg (v)\vert $
with equality if and only if $ v $ is a rational map one might ask whether maps with small …
with equality if and only if $ v $ is a rational map one might ask whether maps with small …
Sharp quantitative stability of the Yamabe problem
H Chen, S Kim - arXiv preprint arXiv:2404.13961, 2024 - arxiv.org
Given a smooth closed Riemannian manifold $(M, g) $ of dimension $ N\ge 3$, we derive
sharp quantitative stability estimates for nonnegative functions near the solution set of the …
sharp quantitative stability estimates for nonnegative functions near the solution set of the …
[PDF][PDF] On the stability of fractional Sobolev trace inequality and corresponding profile decomposition
Y Zhang, Y Zhou, W Zou - arXiv preprint arXiv:2312.01766, 2023 - arxiv.org
In this paper, we study the stability of fractional Sobolev trace inequality within both the
functional and critical point settings. In the functional setting, we establish the following …
functional and critical point settings. In the functional setting, we establish the following …
Degenerate stability of critical points of the Caffarelli-Kohn-Nirenberg inequality along the Felli-Schneider curve
Y Zhou, W Zou - arXiv preprint arXiv:2407.10849, 2024 - arxiv.org
In this paper, we investigate the validity of a quantitative version of stability for the critical
Hardy-H\'enon equation\begin {equation*} H (u):=\div (| x|^{-2a}\nabla u)+| x|^{-pb}| u|^{p-2} …
Hardy-H\'enon equation\begin {equation*} H (u):=\div (| x|^{-2a}\nabla u)+| x|^{-pb}| u|^{p-2} …