Stability with explicit constants of the critical points of the fractional Sobolev inequality and applications to fast diffusion

De Nitti N, König T (2023)

Publication Type: Journal article

Publication year: 2023

Journal

Journal of Functional Analysis Elsevier

Book Volume: 285

Article Number: 110093

Journal Issue: 9

DOI: 10.1016/j.jfa.2023.110093

Abstract

We study the quantitative stability of critical points of the fractional Sobolev inequality. We show that, for a non-negative function u∈H˙^s(R^N) whose energy satisfies [Formula presented]SN,s^{[Formula presented]}≤‖u‖H˙^s(R^N)≤[Formula presented]SN,s^{[Formula presented]}, where SN,s is the optimal Sobolev constant, the bound ‖u−U[z,λ]‖H˙^s(R^N)≲‖(−Δ)^su−u^{2s^⁎−1}‖H˙^−s(R^N), holds for a suitable fractional Talenti bubble U[z,λ]. For functions u which are close to Talenti bubbles, we give the sharp asymptotic value of the implied constant in this inequality. As an application of this, we derive an explicit polynomial extinction rate for positive solutions to a fractional fast diffusion equation.

Authors with CRIS profile

Nicola De Nitti Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Involved external institutions

Goethe-Universität Frankfurt am Main

Germany (DE)

How to cite

APA:

De Nitti, N., & König, T. (2023). Stability with explicit constants of the critical points of the fractional Sobolev inequality and applications to fast diffusion. Journal of Functional Analysis, 285(9). https://dx.doi.org/10.1016/j.jfa.2023.110093

MLA:

De Nitti, Nicola, and Tobias König. "Stability with explicit constants of the critical points of the fractional Sobolev inequality and applications to fast diffusion." Journal of Functional Analysis 285.9 (2023).

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