Improved Sobolev inequality under constraints

2020/10/20 by Fengbo Hang, Xiaodong Wang, Hang, Fengbo +1 · 1 citation
Engineering · Mathematics · #35A23 #53C18 #58C05 #Advanced Numerical Methods in Computational Mathematics #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2010.10654

openalex publication_date 2020/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a new proof of Aubin's improvement of the Sobolev inequality on \mathbbSⁿ under the vanishing of first order moments of the area element and generalize it to higher order moments case. By careful study of an extremal problem on \mathbbSⁿ, we determine the constant explicitly in the second order moments case.

Citations

• Classification of solutions for an integral equation
• Cubature formulas and Sobolev inequalities

Cited by

• Quantitative stability of critical points for the nonlocal-Sobolev inequality in Heisenberg group

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