Wen Yuan

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20242026

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math.AP2026

Sharp Nonlocal Poincaré Inequalities and Liminf Lower Bounds for Sobolev and BV Energies on Metric Measure Spaces

Feng Dai, Tuomas P. Hytönen, Dachun Yang +2

Let $p \in [1, \infty)$ , and let $(X, ρ, μ)$ be a complete doubling $q$ -Poincaré space for some $q \in [1, p]$ with a lower dimension $d$ and an upper dimension $D$ . In this article, we es…

math.AP2026

Sharp Truncated Difference Estimates for Nonlocal Nonconvex Functionals Defined by Superlevel Sets

Feng Dai, Dachun Yang, Wen Yuan +1

Let $N \in N$ and $p \in [1, \infty)$ . In this article, we consider a family ${Φ_{λ, p}^{γ}}_{λ \in (0, \infty)}$ of nonlocal nonconvex functionals with a real parameter $γ$ and est…